{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e.content-description h4 {\n font-size: 1.4em;\n border-bottom: 1px solid #eee;\n line-height: 1.225;\n padding-bottom: 0.3em;\n padding-top: 0.5em;\n font-weight: 700;\n}.content-description img {\n max-width: 100%;\n height: auto;\n}\u003c/style\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"content-description screen\"\u003e\n\u003cdiv\u003e\u003cp\u003eIn a nearby park, there are \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/c1a0bc43a3139849dd28538746a21e7e?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.395ex; height:1.676ex;\" alt\u003d\"n\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~n~\u003c/span\u003e\u003c/span\u003e \u003cstrong\u003efountains\u003c/strong\u003e, labeled from \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e to \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7c2f2bec1ec557e3f5b8a8f76709a8dd?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:5.397ex; height:2.343ex;\" alt\u003d\"n - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~n - 1~\u003c/span\u003e\u003c/span\u003e. We model the fountains as points on a two-dimensional plane. Namely, fountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a4e1016e68b8319096078a41bff14fe0?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:0.802ex; height:2.176ex;\" alt\u003d\"i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~i~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/69db2a1004b4a30d4e34c524ec7b8034?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:15.369ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le n - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le n - 1)~\u003c/span\u003e\u003c/span\u003e is a point \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1faef218e9e4e9713b9f6b0ac479590?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:9.521ex; height:2.843ex;\" alt\u003d\"(x[i], y[i])\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(x[i], y[i])~\u003c/span\u003e\u003c/span\u003e where \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8177b530e70f71f683435b434555fe47?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.426ex; height:2.843ex;\" alt\u003d\"x[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~x[i]~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/33714513e0a821405d91901ecb09b712?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.252ex; height:2.843ex;\" alt\u003d\"y[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~y[i]~\u003c/span\u003e\u003c/span\u003e are \u003cstrong\u003eeven integers\u003c/strong\u003e. The locations of the fountains are all distinct.\u003c/p\u003e\n\u003cp\u003eTimothy the architect has been hired to plan the construction of some \u003cstrong\u003eroads\u003c/strong\u003e and the placement of one \u003cstrong\u003ebench\u003c/strong\u003e per road. A road is a \u003cstrong\u003ehorizontal\u003c/strong\u003e or \u003cstrong\u003evertical\u003c/strong\u003e line segment of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2~\u003c/span\u003e\u003c/span\u003e, whose endpoints are two distinct fountains. The roads should be constructed such that one can travel between any two fountains by moving along roads. Initially, there are no roads in the park.\u003c/p\u003e\n\u003cp\u003eFor each road, \u003cstrong\u003eexactly\u003c/strong\u003e one bench needs to be placed in the park and \u003cstrong\u003eassigned to\u003c/strong\u003e (i.e., face) that road. Each bench must be placed at some point \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/0dbd3a9f8be46a394aadfeb40965090c?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.071ex; height:2.843ex;\" alt\u003d\"(a, b)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a, b)~\u003c/span\u003e\u003c/span\u003e such that \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/3749e26bb0a8aba9067016494a94ccb0?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.23ex; height:1.676ex;\" alt\u003d\"a\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~a~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/6e4cb09ce4221fd4aacc1a80bd343ab5?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:0.998ex; height:2.176ex;\" alt\u003d\"b\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~b~\u003c/span\u003e\u003c/span\u003e are \u003cstrong\u003eodd integers\u003c/strong\u003e. The locations of the benches must be all \u003cstrong\u003edistinct\u003c/strong\u003e. A bench at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/0dbd3a9f8be46a394aadfeb40965090c?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.071ex; height:2.843ex;\" alt\u003d\"(a, b)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a, b)~\u003c/span\u003e\u003c/span\u003e can only be assigned to a road if \u003cstrong\u003eboth\u003c/strong\u003e of the road\u0027s endpoints are among \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/83c0a036293cad77de0643f6caa746f2?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.076ex; height:2.843ex;\" alt\u003d\"(a - 1, b - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a - 1, b - 1)~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/36ebd458eae1c89ddefdbce2661fe144?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.076ex; height:2.843ex;\" alt\u003d\"(a - 1, b + 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a - 1, b + 1)~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d6c71ea7f5f5f6ea2d50c2e634904f89?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.076ex; height:2.843ex;\" alt\u003d\"(a + 1, b - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a + 1, b - 1)~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/ed2b2e92e970ec099d8add9248abbab5?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.076ex; height:2.843ex;\" alt\u003d\"(a + 1, b + 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a + 1, b + 1)~\u003c/span\u003e\u003c/span\u003e. For example, the bench at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d6b6cfdceda24409de39bfdd7ddc1ae5?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(3, 3)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(3, 3)~\u003c/span\u003e\u003c/span\u003e can only be assigned to a road, which is one of the four line segments \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a98c2aaea3d686e113c444a2a1d44993?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.177ex; height:2.843ex;\" alt\u003d\"(2, 2) - (2, 4)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(2, 2) - (2, 4)~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/e7878c7b60e910a263e1adb0fd9e2bf3?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.177ex; height:2.843ex;\" alt\u003d\"(2, 4) - (4, 4)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(2, 4) - (4, 4)~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4905028879557434ea170ab0f3f078e2?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.177ex; height:2.843ex;\" alt\u003d\"(4, 4) - (4, 2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(4, 4) - (4, 2)~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4acd3f297b866ae6a3626d7f0c03ce2d?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:13.177ex; height:2.843ex;\" alt\u003d\"(4, 2) - (2, 2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(4, 2) - (2, 2)~\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eHelp Timothy determine if it is possible to construct roads, and place and assign benches satisfying all conditions given above, and if so, provide him with a feasible solution. If there are multiple feasible solutions that satisfy all conditions, you can report any of them.\u003c/p\u003e\n\u003ch4\u003eImplementation Details\u003c/h4\u003e\n\u003cp\u003eYou should implement the following procedures:\u003c/p\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003econstruct_roads\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e(\u003c/span\u003e\u003cspan class\u003d\"n\"\u003estd\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e::\u003c/span\u003e\u003cspan class\u003d\"n\"\u003evector\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class\u003d\"n\"\u003ex\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"n\"\u003estd\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e::\u003c/span\u003e\u003cspan class\u003d\"n\"\u003evector\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class\u003d\"n\"\u003ey\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e)\u003c/span\u003e\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/c5a1000106524b99ffb20096d04970b1?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.33ex; height:1.676ex;\" alt\u003d\"x\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~x~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/0e8f621bd8562db91042eb6f9f4e6dd4?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:1.155ex; height:2.009ex;\" alt\u003d\"y\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~y~\u003c/span\u003e\u003c/span\u003e: two arrays of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/c1a0bc43a3139849dd28538746a21e7e?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.395ex; height:1.676ex;\" alt\u003d\"n\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~n~\u003c/span\u003e\u003c/span\u003e. For each \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a4e1016e68b8319096078a41bff14fe0?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:0.802ex; height:2.176ex;\" alt\u003d\"i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~i~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/69db2a1004b4a30d4e34c524ec7b8034?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:15.369ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le n - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le n - 1)~\u003c/span\u003e\u003c/span\u003e, fountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a4e1016e68b8319096078a41bff14fe0?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:0.802ex; height:2.176ex;\" alt\u003d\"i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~i~\u003c/span\u003e\u003c/span\u003e is a point \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1faef218e9e4e9713b9f6b0ac479590?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:9.521ex; height:2.843ex;\" alt\u003d\"(x[i], y[i])\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(x[i], y[i])~\u003c/span\u003e\u003c/span\u003e, where \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8177b530e70f71f683435b434555fe47?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.426ex; height:2.843ex;\" alt\u003d\"x[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~x[i]~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/33714513e0a821405d91901ecb09b712?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.252ex; height:2.843ex;\" alt\u003d\"y[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~y[i]~\u003c/span\u003e\u003c/span\u003e are even integers.\u003c/li\u003e\n\u003cli\u003eIf a construction is possible, this procedure should make exactly one call to \u003ccode\u003ebuild\u003c/code\u003e (see below) to report a solution, following which it should return \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003cli\u003eOtherwise, the procedure should return \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e without making any calls to \u003ccode\u003ebuild\u003c/code\u003e.\u003c/li\u003e\n\u003cli\u003eThis procedure is called exactly once.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eYour implementation can call the following procedure to provide a feasible construction of roads and a\nplacement of benches:\u003c/p\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"kt\"\u003evoid\u003c/span\u003e \u003cspan class\u003d\"n\"\u003ebuild\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e(\u003c/span\u003e\u003cspan class\u003d\"n\"\u003estd\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e::\u003c/span\u003e\u003cspan class\u003d\"n\"\u003evector\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eu\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"n\"\u003estd\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e::\u003c/span\u003e\u003cspan class\u003d\"n\"\u003evector\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class\u003d\"n\"\u003ev\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"n\"\u003estd\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e::\u003c/span\u003e\u003cspan class\u003d\"n\"\u003evector\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class\u003d\"n\"\u003ea\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"n\"\u003estd\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e::\u003c/span\u003e\u003cspan class\u003d\"n\"\u003evector\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026lt;\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e\u003cspan class\u003d\"o\"\u003e\u0026gt;\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eb\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e)\u003c/span\u003e\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cul\u003e\n\u003cli\u003eLet \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/22629ccb3d1a5b3099abc5982fa618a2?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.04ex; height:1.676ex;\" alt\u003d\"m\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~m~\u003c/span\u003e\u003c/span\u003e be the total number of roads in the construction.\u003c/li\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/2885caae485b35624f2b49953cb25c3a?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.33ex; height:1.676ex;\" alt\u003d\"u\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~u~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/9a921fcc1a096a8c5d70c1428e2bce78?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.128ex; height:1.676ex;\" alt\u003d\"v\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~v~\u003c/span\u003e\u003c/span\u003e: two arrays of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/22629ccb3d1a5b3099abc5982fa618a2?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.04ex; height:1.676ex;\" alt\u003d\"m\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~m~\u003c/span\u003e\u003c/span\u003e, representing the roads to be constructed. These roads are labeled from \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e to \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/61c420935e1b4cad3cab56e4a1d3c188?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:6.043ex; height:2.343ex;\" alt\u003d\"m - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~m - 1~\u003c/span\u003e\u003c/span\u003e. For each \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1ce794193cf0a31252546069ac934df?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;\" alt\u003d\"j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~j~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/43dbfbd62b4a2773751507430ba42ec1?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:16.17ex; height:2.843ex;\" alt\u003d\"(0 \\le j \\le m - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le m - 1)~\u003c/span\u003e\u003c/span\u003e, road \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1ce794193cf0a31252546069ac934df?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;\" alt\u003d\"j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~j~\u003c/span\u003e\u003c/span\u003e connects fountains \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/c9a78073c8ad50fad573e5e823cf4057?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.581ex; height:2.843ex;\" alt\u003d\"u[j]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~u[j]~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/eea8956212c234aade47dbc988b05af3?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.379ex; height:2.843ex;\" alt\u003d\"v[j]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~v[j]~\u003c/span\u003e\u003c/span\u003e. Each road must be a horizontal or vertical line segment of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2~\u003c/span\u003e\u003c/span\u003e. Any two distinct roads can have at most one point in common (a fountain). Once the roads are constructed, it should be possible to travel between any two fountains by moving along roads.\u003c/li\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/3749e26bb0a8aba9067016494a94ccb0?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.23ex; height:1.676ex;\" alt\u003d\"a\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~a~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/6e4cb09ce4221fd4aacc1a80bd343ab5?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:0.998ex; height:2.176ex;\" alt\u003d\"b\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~b~\u003c/span\u003e\u003c/span\u003e: two arrays of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/22629ccb3d1a5b3099abc5982fa618a2?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.04ex; height:1.676ex;\" alt\u003d\"m\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~m~\u003c/span\u003e\u003c/span\u003e, representing the benches. For each \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1ce794193cf0a31252546069ac934df?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;\" alt\u003d\"j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~j~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/43dbfbd62b4a2773751507430ba42ec1?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:16.17ex; height:2.843ex;\" alt\u003d\"(0 \\le j \\le m - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le m - 1)~\u003c/span\u003e\u003c/span\u003e, a bench is placed at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/e26043ac0fdc2cafe0f35128dac682a4?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:9.574ex; height:2.843ex;\" alt\u003d\"(a[j], b[j])\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(a[j], b[j])~\u003c/span\u003e\u003c/span\u003e, and is assigned to road \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1ce794193cf0a31252546069ac934df?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;\" alt\u003d\"j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~j~\u003c/span\u003e\u003c/span\u003e. No two distinct benches can have the same location.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch4\u003eExamples\u003c/h4\u003e\n\u003ch5\u003eExample 1\u003c/h5\u003e\n\u003cp\u003eConsider the following call:\u003c/p\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"n\"\u003econstruct_roads\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e({\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e6\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e2\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e},\u003c/span\u003e \u003cspan class\u003d\"p\"\u003e{\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e6\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e2\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e})\u003c/span\u003e\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp\u003eThis means that there are \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d507316514f40c32c45d33bbb3875b0e?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"5\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~5~\u003c/span\u003e\u003c/span\u003e fountains:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003efountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/298ac0020c655cf69fdc0eded04666be?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(4, 4)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(4, 4)~\u003c/span\u003e\u003c/span\u003e,\u003c/li\u003e\n\u003cli\u003efountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/66455ba97f2a04775b1260bb3abb20cf?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(4, 6)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(4, 6)~\u003c/span\u003e\u003c/span\u003e,\u003c/li\u003e\n\u003cli\u003efountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/27a06ae082188a3ced1d8c95a5360540?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(6, 4)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(6, 4)~\u003c/span\u003e\u003c/span\u003e,\u003c/li\u003e\n\u003cli\u003efountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/86748ce269b76185f219ba13eeede716?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"3\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~3~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/1152e2b4737457db21b8d98cc9d98e18?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(4, 2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(4, 2)~\u003c/span\u003e\u003c/span\u003e,\u003c/li\u003e\n\u003cli\u003efountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/acf1b79c1849c49564c7ac0004e5c5e3?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"4\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~4~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dd961f2a0d541ecf0d8a56091215da7b?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(2, 4)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(2, 4)~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIt is possible to construct the following \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/acf1b79c1849c49564c7ac0004e5c5e3?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"4\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~4~\u003c/span\u003e\u003c/span\u003e roads, where each road connects two fountains, and place the corresponding benches:\u003c/p\u003e\n\u003ctable class\u003d\"table\" style\u003d\"max-width:50%;\"\u003e\n\u003ctbody\u003e\u003ctr\u003e\n\u003cth\u003eRoad label\u003c/th\u003e\n\u003cth\u003eLabels of the fountains the road connects\u003c/th\u003e\n\u003cth\u003eLocation of the assigned bench\u003c/th\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/2b594e074107e4c1f97d0f1220c599e2?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"0, 2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0, 2~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/916bb589dae1c8af2e1f0452a81603f8?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"5, 5\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~5, 5~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a93062e9804a97b2252780df07489b0c?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"0, 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0, 1~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/569f89525a5f107d343738ab04a787af?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"3, 5\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~3, 5~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d3ba2db2ad99018b2c717a2ad6444101?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"3, 0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~3, 0~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d2705d3b9eabd0c6820295ab658b6f28?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"5, 3\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~5, 3~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/86748ce269b76185f219ba13eeede716?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"3\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~3~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/79e62fb74dcdbd9b8cb0e6aa6442c244?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"4, 0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~4, 0~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003ctd\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/09c6101949d401faf5daa54aa60fedc4?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:3.359ex; height:2.509ex;\" alt\u003d\"3, 3\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~3, 3~\u003c/span\u003e\u003c/span\u003e\u003c/td\u003e\n\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003cp\u003eThis solution corresponds to the following diagram:\u003c/p\u003e\n\u003cdiv style\u003d\"margin: auto; padding: 20px; width: 800px;\"\u003e\n\u003cimg src\u003d\"CDN_BASE_URL/34f2a1cf72ee41a214175932ec8d51c4?v\u003d1715136347\" alt\u003e\u003c/div\u003e\u003cp\u003eTo report this solution, \u003ccode\u003econstruct_roads\u003c/code\u003e should make the following call:\u003c/p\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"n\"\u003ebuild\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e({\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e0\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e0\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e3\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e},\u003c/span\u003e \u003cspan class\u003d\"p\"\u003e{\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e2\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e1\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e0\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e0\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e},\u003c/span\u003e \u003cspan class\u003d\"p\"\u003e{\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e5\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e3\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e5\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e3\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e},\u003c/span\u003e \u003cspan class\u003d\"p\"\u003e{\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e5\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e5\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e3\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e3\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e})\u003c/span\u003e\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp\u003eIt should then return \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eNote that in this case, there are multiple solutions that satisfy the requirements, all of which would be considered correct. For example, it is also correct to call \u003ccode\u003ebuild({1, 2, 3, 4}, {0, 0, 0, 0}, {5, 5, 3, 3}, {5, 3, 3, 5})\u003c/code\u003e and then return \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003ch5\u003eExample 2\u003c/h5\u003e\n\u003cp\u003eConsider the following call:\u003c/p\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"n\"\u003econstruct_roads\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e({\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e2\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e4\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e},\u003c/span\u003e \u003cspan class\u003d\"p\"\u003e{\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e2\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"mi\"\u003e6\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e})\u003c/span\u003e\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp\u003eFountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/9e022ff83838a36bb4e64253a8f59075?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(2, 2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(2, 2)~\u003c/span\u003e\u003c/span\u003e and fountain \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e is located at \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/66455ba97f2a04775b1260bb3abb20cf?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:5.168ex; height:2.843ex;\" alt\u003d\"(4, 6)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(4, 6)~\u003c/span\u003e\u003c/span\u003e. Since there is no way to construct roads that satisfy the requirements, \u003ccode\u003econstruct_roads\u003c/code\u003e should return \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0~\u003c/span\u003e\u003c/span\u003e without making any call to \u003ccode\u003ebuild\u003c/code\u003e.\u003c/p\u003e\n\u003ch4\u003eConstraints\u003c/h4\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/2f059c2d9dd092a58034a1f4117ac292?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:16.116ex; height:2.343ex;\" alt\u003d\"1 \\le n \\le 200\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1 \\le n \\le 200\\,000~\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4dcdfd53b1098130897007703c58b9b9?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:22.433ex; height:2.843ex;\" alt\u003d\"2 \\le x[i], y[i] \\le 200\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2 \\le x[i], y[i] \\le 200\\,000~\u003c/span\u003e\u003c/span\u003e (for all \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a49750dff2c898b533a2d07297b07442?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:13.56ex; height:2.343ex;\" alt\u003d\"0 \\le i \\le n - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le i \\le n - 1~\u003c/span\u003e\u003c/span\u003e)\u003c/li\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8177b530e70f71f683435b434555fe47?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.426ex; height:2.843ex;\" alt\u003d\"x[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~x[i]~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/33714513e0a821405d91901ecb09b712?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:3.252ex; height:2.843ex;\" alt\u003d\"y[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~y[i]~\u003c/span\u003e\u003c/span\u003e are even integers (for all \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a49750dff2c898b533a2d07297b07442?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:13.56ex; height:2.343ex;\" alt\u003d\"0 \\le i \\le n - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le i \\le n - 1~\u003c/span\u003e\u003c/span\u003e)\u003c/li\u003e\n\u003cli\u003eNo two fountains have the same location.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch4\u003eSubtasks\u003c/h4\u003e\n\u003col\u003e\n\u003cli\u003e(\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d507316514f40c32c45d33bbb3875b0e?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"5\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~5~\u003c/span\u003e\u003c/span\u003e points) \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/e8b7c4be6b94acd7740f464abab3d9b1?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:7.687ex; height:2.843ex;\" alt\u003d\"x[i] \u003d 2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~x[i] \u003d 2~\u003c/span\u003e\u003c/span\u003e (for all \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a49750dff2c898b533a2d07297b07442?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:13.56ex; height:2.343ex;\" alt\u003d\"0 \\le i \\le n - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le i \\le n - 1~\u003c/span\u003e\u003c/span\u003e)\u003c/li\u003e\n\u003cli\u003e(\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/e604467303f21c656febff5848d33242?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"10\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~10~\u003c/span\u003e\u003c/span\u003e points) \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8062359052579dd91278e147dbd208ff?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:11.948ex; height:2.843ex;\" alt\u003d\"2 \\le x[i] \\le 4\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2 \\le x[i] \\le 4~\u003c/span\u003e\u003c/span\u003e (for all \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a49750dff2c898b533a2d07297b07442?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:13.56ex; height:2.343ex;\" alt\u003d\"0 \\le i \\le n - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le i \\le n - 1~\u003c/span\u003e\u003c/span\u003e)\u003c/li\u003e\n\u003cli\u003e(\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/1cf3841d7831a1b2614025a120ce18f7?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"15\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~15~\u003c/span\u003e\u003c/span\u003e points) \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/db94f4edf6a6cb40824d55048fa24e8e?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:11.948ex; height:2.843ex;\" alt\u003d\"2 \\le x[i] \\le 6\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2 \\le x[i] \\le 6~\u003c/span\u003e\u003c/span\u003e (for all \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a49750dff2c898b533a2d07297b07442?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:13.56ex; height:2.343ex;\" alt\u003d\"0 \\le i \\le n - 1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le i \\le n - 1~\u003c/span\u003e\u003c/span\u003e)\u003c/li\u003e\n\u003cli\u003e(\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/300ead7f8aa7ceb0318f9280015eb55b?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"20\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~20~\u003c/span\u003e\u003c/span\u003e points) There is at most one way of constructing the roads, such that one can travel between any two fountains by moving along roads.\u003c/li\u003e\n\u003cli\u003e(\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/300ead7f8aa7ceb0318f9280015eb55b?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"20\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~20~\u003c/span\u003e\u003c/span\u003e points) There do not exist four fountains that form the corners of a \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/0f0b5bb02fc82a8c9f27d11078fcd245?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:5.165ex; height:2.176ex;\" alt\u003d\"2 \\times 2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2 \\times 2~\u003c/span\u003e\u003c/span\u003e square.\u003c/li\u003e\n\u003cli\u003e(\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8434eb29a7dd42118f81acbb1c14fc36?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"30\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~30~\u003c/span\u003e\u003c/span\u003e points) No additional constraints.\u003c/li\u003e\n\u003c/ol\u003e\n\u003ch4\u003eSample Grader\u003c/h4\u003e\n\u003cp\u003eThe sample grader reads the input in the following format:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eline \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e: \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/c1a0bc43a3139849dd28538746a21e7e?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.395ex; height:1.676ex;\" alt\u003d\"n\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~n~\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003cli\u003eline \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dd6a26d205d1ff5b8c800dba21ce18af?v\u003d1715136347\" style\u003d\"vertical-align: -0.505ex; width:4.805ex; height:2.343ex;\" alt\u003d\"2 + i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2 + i~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/69db2a1004b4a30d4e34c524ec7b8034?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:15.369ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le n - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le n - 1)~\u003c/span\u003e\u003c/span\u003e: \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8bb46c734f498d8e92f575c95a08ec2b?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:7.258ex; height:2.843ex;\" alt\u003d\"x[i] \\ y[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~x[i] \\ y[i]~\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe output of the sample grader is in the following format:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eline \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e: the return value of \u003ccode\u003econstruct_roads\u003c/code\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eIf the return value of \u003ccode\u003econstruct_roads\u003c/code\u003e is \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1~\u003c/span\u003e\u003c/span\u003e and \u003ccode\u003ebuild(u, v, a, b)\u003c/code\u003e is called, the grader then additionally prints:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eline \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2~\u003c/span\u003e\u003c/span\u003e: \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/22629ccb3d1a5b3099abc5982fa618a2?v\u003d1715136347\" style\u003d\"vertical-align: -0.338ex; width:2.04ex; height:1.676ex;\" alt\u003d\"m\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~m~\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003cli\u003eline \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/ccb47af3c6149902207077af0194ffcf?v\u003d1715136347\" style\u003d\"vertical-align: -0.671ex; width:4.961ex; height:2.509ex;\" alt\u003d\"3 + j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~3 + j~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/43dbfbd62b4a2773751507430ba42ec1?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:16.17ex; height:2.843ex;\" alt\u003d\"(0 \\le j \\le m - 1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le m - 1)~\u003c/span\u003e\u003c/span\u003e: \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4e6626c581f67c48386f18d38578ea8b?v\u003d1715136347\" style\u003d\"vertical-align: -0.838ex; width:15.434ex; height:2.843ex;\" alt\u003d\"u[j] \\ v[j] \\ a[j] \\ b[j]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~u[j] \\ v[j] \\ a[j] \\ b[j]~\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch4\u003eAttachment Package\u003c/h4\u003e\n\u003cp\u003eThe sample grader and sample test cases are available here: \u003ca href\u003d\"https://static.dmoj.ca/data/ioi/21/ioi21p3/parks.zip\"\u003eparks.zip\u003c/a\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\n\u003c/div\u003e"}}]}