{"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\u003ch5\u003eContest Day 1 - JOI Open Contest\u003c/h5\u003e\n\u003cp\u003eIn IOI Kingdom, there are \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7b60d7c68d7ec066966b2e5a535229a8?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:2.064ex; height:2.176ex;\" alt\u003d\"N\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~N~\u003c/span\u003e\u003c/span\u003e cities numbered from \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1714823840\" 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/fd8b3536ed085708a0178c8e31f8cf22?v\u003d1714823840\" style\u003d\"vertical-align: -0.505ex; width:6.066ex; 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. These cities are connected by \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fd8b3536ed085708a0178c8e31f8cf22?v\u003d1714823840\" style\u003d\"vertical-align: -0.505ex; width:6.066ex; 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 roads through which you can pass in both directions. You can travel from any city to any other city by passing through some of these roads.\u003c/p\u003e\n\u003cp\u003eIn IOI Kingdom, there are many companies producing special components. Each company produces only one kind of components. No two companies produce the same kind of components. Each company has at least one factory. Each factory is built in one of the cities. More than one company may have factories in the same city.\u003c/p\u003e\n\u003cp\u003eSometimes, a company requires components of another company. Assume the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7b3e7df1f2a5d8b4f304f5c2f02bf49f?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:3.127ex; height:2.509ex;\" alt\u003d\"C_A\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~C_A~\u003c/span\u003e\u003c/span\u003e requires the components of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/44d751b80c3f9589bf9c97a41709dc90?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:3.141ex; height:2.509ex;\" alt\u003d\"C_B\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~C_B~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/351bc1f06c464ae5986ad42d9adf201f?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:11.176ex; height:2.843ex;\" alt\u003d\"(C_A \\ne C_B)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(C_A \\ne C_B)~\u003c/span\u003e\u003c/span\u003e. In this case, they need to transport components from \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/44d751b80c3f9589bf9c97a41709dc90?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:3.141ex; height:2.509ex;\" alt\u003d\"C_B\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~C_B~\u003c/span\u003e\u003c/span\u003e to \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7b3e7df1f2a5d8b4f304f5c2f02bf49f?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:3.127ex; height:2.509ex;\" alt\u003d\"C_A\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~C_A~\u003c/span\u003e\u003c/span\u003e. They may transport components from any of the factories of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/44d751b80c3f9589bf9c97a41709dc90?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:3.141ex; height:2.509ex;\" alt\u003d\"C_B\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~C_B~\u003c/span\u003e\u003c/span\u003e to any of the factories of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7b3e7df1f2a5d8b4f304f5c2f02bf49f?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:3.127ex; height:2.509ex;\" alt\u003d\"C_A\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~C_A~\u003c/span\u003e\u003c/span\u003e. They need to choose factories appropriately to minimize the distance between factories.\u003c/p\u003e\n\u003ch4\u003eTask\u003c/h4\u003e\n\u003cp\u003eFirst, the number of cities and the information of roads in IOI Kingdom are given. Then, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d8d5cff7eb1238d9dec4f7a0a8e840be?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:1.838ex; height:2.509ex;\" alt\u003d\"Q\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~Q~\u003c/span\u003e\u003c/span\u003e queries are given. Each query is written in the following form: the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/93d8e4a5c0f3847a6ea6a75fb8095cad?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.497ex; 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 having factories in cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/ae65c2d6612731a3f95304f6c9a1f2c5?v\u003d1714823840\" style\u003d\"vertical-align: -1.171ex; width:16.405ex; height:3.009ex;\" alt\u003d\"X_{j,0}, \\dots, X_{j,S_j-1}\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~X_{j,0}, \\dots, X_{j,S_j-1}~\u003c/span\u003e\u003c/span\u003e requires components of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4c5ec72a8bf85b85cae70b2f7421012f?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.265ex; 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 having factories in cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/6c6186b3459f78cba90804c2ab31e7fa?v\u003d1714823840\" style\u003d\"vertical-align: -1.171ex; width:15.21ex; height:3.009ex;\" alt\u003d\"Y_{j, 0}, \\dots, Y_{j,T_j-1}\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~Y_{j, 0}, \\dots, Y_{j,T_j-1}~\u003c/span\u003e\u003c/span\u003e. Write a program which, for each query, returns the minimum distance to transport the components.\u003c/p\u003e\n\u003ch4\u003eImplementation Details\u003c/h4\u003e\n\u003cp\u003eYou are to write a program which implements procedures to answer queries.\u003cbr\u003e\nYour program should include the header file \u003ccode\u003efactories.h\u003c/code\u003e by \u003ccode\u003e#include \"factories.h\"\u003c/code\u003e\u003cbr\u003e\nYour program 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\"\u003evoid\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eInit\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e(\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eN\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eA\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e[],\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eB\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e[],\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eD\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\u003eThis procedure is called only once in the beginning. The parameter \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7b60d7c68d7ec066966b2e5a535229a8?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:2.064ex; height:2.176ex;\" alt\u003d\"N\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~N~\u003c/span\u003e\u003c/span\u003e is the number of cities in IOI Kingdom. The parameters \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/028749d5e836ddd64cf7b64cde5d5b01?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.743ex; height:2.176ex;\" 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/3dfcbca04b4565af0bc3043c18f7c3a7?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.764ex; height:2.176ex;\" alt\u003d\"B\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~B~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/88e23bbd88480da27de8c22b113d8b7b?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.924ex; height:2.176ex;\" alt\u003d\"D\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~D~\u003c/span\u003e\u003c/span\u003e are arrays of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fd8b3536ed085708a0178c8e31f8cf22?v\u003d1714823840\" style\u003d\"vertical-align: -0.505ex; width:6.066ex; 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. The elements \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dda15d3d18091e2500d3012a5c362ce2?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:3.839ex; height:2.843ex;\" alt\u003d\"A[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~A[i]~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/1e5af5527b25557afcd4182a2c3572dd?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:3.86ex; height:2.843ex;\" alt\u003d\"B[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~B[i]~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fb855a60f6be813b92fe54a06ddd85ac?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:4.02ex; height:2.843ex;\" alt\u003d\"D[i]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~D[i]~\u003c/span\u003e\u003c/span\u003e are three integers \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/9d2b4c2f49a53673c6b5b9504a529f94?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.543ex; height:2.509ex;\" alt\u003d\"A_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~A_i~\u003c/span\u003e\u003c/span\u003e, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/3a0e0637037a63e66188e0f49877c9db?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.564ex; height:2.509ex;\" alt\u003d\"B_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~B_i~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/b043484b05c8deb4cb81fb1545cab973?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.724ex; height:2.509ex;\" alt\u003d\"D_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~D_i~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/07bf14f3cc91c5c4de87734015daf12c?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:16.038ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le N-2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le N-2)~\u003c/span\u003e\u003c/span\u003e respectively. This means, for each \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a4e1016e68b8319096078a41bff14fe0?v\u003d1714823840\" 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/07bf14f3cc91c5c4de87734015daf12c?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:16.038ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le N-2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le N-2)~\u003c/span\u003e\u003c/span\u003e, there is a road of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/b043484b05c8deb4cb81fb1545cab973?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.724ex; height:2.509ex;\" alt\u003d\"D_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~D_i~\u003c/span\u003e\u003c/span\u003e connecting the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/9d2b4c2f49a53673c6b5b9504a529f94?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.543ex; height:2.509ex;\" alt\u003d\"A_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~A_i~\u003c/span\u003e\u003c/span\u003e and the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/3a0e0637037a63e66188e0f49877c9db?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.564ex; height:2.509ex;\" alt\u003d\"B_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~B_i~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"kt\"\u003elong\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003elong\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eQuery\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e(\u003c/span\u003e\u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eS\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eX\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e[],\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003eint\u003c/span\u003e \u003cspan class\u003d\"n\"\u003eT\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\u003c/span\u003e \u003cspan class\u003d\"kt\"\u003eint\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\u003eThis procedure is called for each of \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d8d5cff7eb1238d9dec4f7a0a8e840be?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:1.838ex; height:2.509ex;\" alt\u003d\"Q\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~Q~\u003c/span\u003e\u003c/span\u003e queries. In the query \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1ce794193cf0a31252546069ac934df?v\u003d1714823840\" 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, the parameters \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/88f6074530170d626706a50a8ec2af58?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.499ex; height:2.176ex;\" alt\u003d\"S\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~S~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/6cc00c87382662dc277f1e589dba9882?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.636ex; height:2.176ex;\" alt\u003d\"T\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~T~\u003c/span\u003e\u003c/span\u003e are two integers \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a42f2ea95511cfa801b08546fa66d63e?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.335ex; height:2.843ex;\" alt\u003d\"S_j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~S_j~\u003c/span\u003e\u003c/span\u003e and \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/46bcc01222909cc5cc192485e52ee5c5?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.267ex; height:2.843ex;\" alt\u003d\"T_j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~T_j~\u003c/span\u003e\u003c/span\u003e respectively. These are the numbers of cities where the companies \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/93d8e4a5c0f3847a6ea6a75fb8095cad?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.497ex; 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, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4c5ec72a8bf85b85cae70b2f7421012f?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.265ex; 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 have factories respectively. The parameter \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/094969d499cf288952117cb6d5f341a6?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.98ex; height:2.176ex;\" alt\u003d\"X\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~X~\u003c/span\u003e\u003c/span\u003e is an array of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a42f2ea95511cfa801b08546fa66d63e?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.335ex; height:2.843ex;\" alt\u003d\"S_j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~S_j~\u003c/span\u003e\u003c/span\u003e. The company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/93d8e4a5c0f3847a6ea6a75fb8095cad?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.497ex; 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 has factories in cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/2cadb222a59f41fd9dfa1db0a73a4c67?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:23.86ex; height:2.843ex;\" alt\u003d\"X[0], X[1], \\dots, X[S-1]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~X[0], X[1], \\dots, X[S-1]~\u003c/span\u003e\u003c/span\u003e.\nThe parameter \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/a632184e023975ae276dfac5ea016755?v\u003d1714823840\" style\u003d\"vertical-align: -0.171ex; width:1.773ex; height:2.009ex;\" alt\u003d\"Y\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~Y~\u003c/span\u003e\u003c/span\u003e is an array of length \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/46bcc01222909cc5cc192485e52ee5c5?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.267ex; height:2.843ex;\" alt\u003d\"T_j\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~T_j~\u003c/span\u003e\u003c/span\u003e. The company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4c5ec72a8bf85b85cae70b2f7421012f?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.265ex; 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 has factories in cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7c6696b79c6495a33f3cefeefa5e1b0c?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:23.377ex; height:2.843ex;\" alt\u003d\"Y[0], Y[1], \\dots, Y[T-1]\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~Y[0], Y[1], \\dots, Y[T-1]~\u003c/span\u003e\u003c/span\u003e.\u003cbr\u003e\nThis procedure should return the minimum distance to transport components from the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4c5ec72a8bf85b85cae70b2f7421012f?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.265ex; 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 to the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/93d8e4a5c0f3847a6ea6a75fb8095cad?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:2.497ex; 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.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch4\u003eConstraints\u003c/h4\u003e\n\u003cp\u003eAll input data satisfy the following conditions:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d1825e8598ed3c54e9645d29755ec0bd?v\u003d1714823840\" style\u003d\"vertical-align: -0.505ex; width:16.785ex; height:2.343ex;\" alt\u003d\"2 \\le N \\le 500\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~2 \\le N \\le 500\\,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/da30eef818cc02a9d06bfd48cb385590?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:16.56ex; height:2.509ex;\" alt\u003d\"1 \\le Q \\le 100\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1 \\le Q \\le 100\\,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/c7efc05cf20c4d976f632d4f643d2257?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:15.969ex; height:2.509ex;\" alt\u003d\"0 \\le A_i \\le N-1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le A_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/07bf14f3cc91c5c4de87734015daf12c?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:16.038ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le N-2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le N-2)~\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/617b1e288dc67e3e9096d09073fdd4ad?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:15.99ex; height:2.509ex;\" alt\u003d\"0 \\le B_i \\le N-1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le B_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/07bf14f3cc91c5c4de87734015daf12c?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:16.038ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le N-2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le N-2)~\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/a05c40d7e563012da63faf62f9d2ce53?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:21.32ex; height:2.509ex;\" alt\u003d\"1 \\le D_i \\le 100\\,000\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1 \\le D_i \\le 100\\,000\\,000~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/07bf14f3cc91c5c4de87734015daf12c?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:16.038ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le N-2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le N-2)~\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/fc2e58b9922ed5d0e1db8ddfed7fcdee?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:8.205ex; height:2.676ex;\" alt\u003d\"A_i \\ne B_i\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~A_i \\ne B_i~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/78cd37cf35887b1676a0bc3ea9f9ef3f?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:16.038ex; height:2.843ex;\" alt\u003d\"(1 \\le i \\le N-2)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(1 \\le i \\le N-2)~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003cli\u003eYou can travel from any city to any other city through some of these roads.\u003c/li\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/f44100af053ea59ba0298b22ac030eeb?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:15.761ex; height:2.843ex;\" alt\u003d\"1 \\le S_j \\le N-1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1 \\le S_j \\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/ac03fcc6075908084355d0dbf05c4f6b?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:15.968ex; height:2.843ex;\" alt\u003d\"(0 \\le j \\le Q-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le Q-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/ff1021865c1e17f6096c1a6206a39840?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:17.574ex; height:2.843ex;\" alt\u003d\"0 \\le X_{j,k} \\le N-1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le X_{j,k} \\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/16212d315ef0975e0b56d43a6e0fe4c5?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:31.91ex; height:3.009ex;\" alt\u003d\"(0 \\le j \\le Q-1, 0 \\le k \\le S_j-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le Q-1, 0 \\le k \\le S_j-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/1a1940123a6a5bab1b0518290b7ecbf3?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:15.693ex; height:2.843ex;\" alt\u003d\"1 \\le T_j \\le N-1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~1 \\le T_j \\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/ac03fcc6075908084355d0dbf05c4f6b?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:15.968ex; height:2.843ex;\" alt\u003d\"(0 \\le j \\le Q-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le Q-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/9eee4762b77c01f14d42fc9e31b5087e?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:17ex; height:2.843ex;\" alt\u003d\"0 \\le Y_{j,k} \\le N-1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~0 \\le Y_{j,k} \\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/9ca0d8eadf1a5fe44c03a4bd16bcfc2a?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:31.843ex; height:3.009ex;\" alt\u003d\"(0 \\le j \\le Q-1, 0 \\le k \\le T_j-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le Q-1, 0 \\le k \\le T_j-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/3acc4328e2b83f2005ae136e94532188?v\u003d1714823840\" style\u003d\"vertical-align: -1.171ex; width:42.371ex; height:3.009ex;\" alt\u003d\"X_{j,0}, X_{j,1}, \\dots, X_{j, S_j-1}, Y_{j,0}, Y_{j,1}, \\dots, Y_{j, T_j-1}\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~X_{j,0}, X_{j,1}, \\dots, X_{j, S_j-1}, Y_{j,0}, Y_{j,1}, \\dots, Y_{j, T_j-1}~\u003c/span\u003e\u003c/span\u003e are different from each other \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/ac03fcc6075908084355d0dbf05c4f6b?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:15.968ex; height:2.843ex;\" alt\u003d\"(0 \\le j \\le Q-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le j \\le Q-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/a91b4e7ceff10c611940b688ecc952b9?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:33.27ex; height:2.843ex;\" alt\u003d\"S_0 + S_1 + \\dots + S_{Q-1} \\le 1\\,000\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~S_0 + S_1 + \\dots + S_{Q-1} \\le 1\\,000\\,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/66b4df55e43bc64148a8a16864f02a2e?v\u003d1714823840\" style\u003d\"vertical-align: -1.005ex; width:33.068ex; height:2.843ex;\" alt\u003d\"T_0 + T_1 + \\dots + T_{Q-1} \\le 1\\,000\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~T_0 + T_1 + \\dots + T_{Q-1} \\le 1\\,000\\,000~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch5\u003eSubtask 1 [15 points]\u003c/h5\u003e\n\u003cp\u003eThe following conditions are satisfied:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/70be721225cf3a7f35201acd8f3803c7?v\u003d1714823840\" style\u003d\"vertical-align: -0.505ex; width:10.199ex; height:2.343ex;\" alt\u003d\"N \\le 5\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~N \\le 5\\,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/bd8c7d621d80bf38432be300972d88e3?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:9.974ex; height:2.509ex;\" alt\u003d\"Q \\le 5\\,000\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~Q \\le 5\\,000~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch5\u003eSubtask 2 [18 points]\u003c/h5\u003e\n\u003cp\u003eThe following conditions are satisfied.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/8f9074979812de2c1e07f52380a844b4?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:7.648ex; height:2.509ex;\" alt\u003d\"S_i \\le 20\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~S_i \\le 20~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/553bdb9663843042c3f38a8e8e3ac85e?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:15.812ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le Q-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le Q-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/29dc2dd23b4d2c6b9628c9d831af4c5f?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:7.581ex; height:2.509ex;\" alt\u003d\"T_i \\le 20\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~T_i \\le 20~\u003c/span\u003e\u003c/span\u003e \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/553bdb9663843042c3f38a8e8e3ac85e?v\u003d1714823840\" style\u003d\"vertical-align: -0.838ex; width:15.812ex; height:2.843ex;\" alt\u003d\"(0 \\le i \\le Q-1)\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~(0 \\le i \\le Q-1)~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch5\u003eSubtask 3 [67 points]\u003c/h5\u003e\n\u003cp\u003eNo additional constraints.\u003c/p\u003e\n\u003ch4\u003eSample Execution\u003c/h4\u003e\n\u003cdiv class\u003d\"codehilite\"\u003e\u003cpre\u003e\u003cspan\u003e\u003c/span\u003e\u003ccode\u003e\u003cspan class\u003d\"n\"\u003eInit\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e(\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e7\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\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\"\u003e1\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\"\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\"mi\"\u003e1\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e},\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\"\u003e2\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\"mi\"\u003e5\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\"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\"\u003e5\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\"\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\n\u003cspan class\u003d\"n\"\u003eQuery\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\"\u003e0\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\"\u003e2\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e,\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\"c1\"\u003e//returns 12.\u003c/span\u003e\n\u003cspan class\u003d\"n\"\u003eQuery\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\"\u003e0\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\"\u003e3\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\"c1\"\u003e//returns 3.\u003c/span\u003e\n\u003cspan class\u003d\"n\"\u003eQuery\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\"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\"p\"\u003e{\u003c/span\u003e\u003cspan class\u003d\"mi\"\u003e5\u003c/span\u003e\u003cspan class\u003d\"p\"\u003e});\u003c/span\u003e \u003cspan class\u003d\"c1\"\u003e//returns 11.\u003c/span\u003e\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003ch4\u003eExplanation for Sample\u003c/h4\u003e\n\u003cp\u003eThese are sample input and sample output of the sample grader.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eIn query \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1714823840\" 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, the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/e18fc2de82eb615588f6c961bbc3a02a?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.642ex; height:2.509ex;\" alt\u003d\"U_0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~U_0~\u003c/span\u003e\u003c/span\u003e has factories in the cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1714823840\" 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, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/b971e4e8d7ad61ebfaa4c68650093f06?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"6\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~6~\u003c/span\u003e\u003c/span\u003e, and the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4733f6a986eab4e79629b68e9872f224?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.409ex; height:2.509ex;\" alt\u003d\"V_0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~V_0~\u003c/span\u003e\u003c/span\u003e has factories in the cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/86748ce269b76185f219ba13eeede716?v\u003d1714823840\" 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, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/acf1b79c1849c49564c7ac0004e5c5e3?v\u003d1714823840\" 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. The distance from the factory of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/4733f6a986eab4e79629b68e9872f224?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.409ex; height:2.509ex;\" alt\u003d\"V_0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~V_0~\u003c/span\u003e\u003c/span\u003e in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/86748ce269b76185f219ba13eeede716?v\u003d1714823840\" 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 to the factory of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/e18fc2de82eb615588f6c961bbc3a02a?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.642ex; height:2.509ex;\" alt\u003d\"U_0\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~U_0~\u003c/span\u003e\u003c/span\u003e in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/b971e4e8d7ad61ebfaa4c68650093f06?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"6\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~6~\u003c/span\u003e\u003c/span\u003e is minimum. The minimum distance is \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/95af0f0b925a5fe7f64a53e52950b0e1?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"12\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~12~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003cli\u003eIn the query \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1714823840\" 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 company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/cfeca2a4857e40cc2eb52afe0b8a38f7?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.642ex; height:2.509ex;\" alt\u003d\"U_1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~U_1~\u003c/span\u003e\u003c/span\u003e has factories in the cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/fc9653f00347ae032c0bb3370a2c7a76?v\u003d1714823840\" 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, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1714823840\" 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/86748ce269b76185f219ba13eeede716?v\u003d1714823840\" 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, and the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/9ebadc7edc8800a6ea1f5338ee009099?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.409ex; height:2.509ex;\" alt\u003d\"V_1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~V_1~\u003c/span\u003e\u003c/span\u003e has factories in the cities \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/acf1b79c1849c49564c7ac0004e5c5e3?v\u003d1714823840\" 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, \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/b971e4e8d7ad61ebfaa4c68650093f06?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"6\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~6~\u003c/span\u003e\u003c/span\u003e. The distance from the factory of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/9ebadc7edc8800a6ea1f5338ee009099?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.409ex; height:2.509ex;\" alt\u003d\"V_1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~V_1~\u003c/span\u003e\u003c/span\u003e in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/b971e4e8d7ad61ebfaa4c68650093f06?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:1.162ex; height:2.176ex;\" alt\u003d\"6\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~6~\u003c/span\u003e\u003c/span\u003e to the factory of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/cfeca2a4857e40cc2eb52afe0b8a38f7?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.642ex; height:2.509ex;\" alt\u003d\"U_1\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~U_1~\u003c/span\u003e\u003c/span\u003e in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/dc15aebf4fa2f4039e7e91a157d4b279?v\u003d1714823840\" 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 minimum. The minimum distance is \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/86748ce269b76185f219ba13eeede716?v\u003d1714823840\" 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/li\u003e\n\u003cli\u003eIn the query \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1714823840\" 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, the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/82ab34a5373f612156ac76c7e6a83fa7?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.642ex; height:2.509ex;\" alt\u003d\"U_2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~U_2~\u003c/span\u003e\u003c/span\u003e has factories in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1714823840\" 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, and the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7c3600f8443d2569ee8198d7f76ca12f?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.409ex; height:2.509ex;\" alt\u003d\"V_2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~V_2~\u003c/span\u003e\u003c/span\u003e has factories in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d507316514f40c32c45d33bbb3875b0e?v\u003d1714823840\" 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. The distance from the factory of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/7c3600f8443d2569ee8198d7f76ca12f?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.409ex; height:2.509ex;\" alt\u003d\"V_2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~V_2~\u003c/span\u003e\u003c/span\u003e in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d507316514f40c32c45d33bbb3875b0e?v\u003d1714823840\" 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 to the factory of the company \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/82ab34a5373f612156ac76c7e6a83fa7?v\u003d1714823840\" style\u003d\"vertical-align: -0.671ex; width:2.642ex; height:2.509ex;\" alt\u003d\"U_2\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~U_2~\u003c/span\u003e\u003c/span\u003e in the city \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/edff4a53ceab26bbeb9fa3434bd9765d?v\u003d1714823840\" 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 minimum. The minimum distance is \u003cspan class\u003d\"inline-math\"\u003e\u003cimg class\u003d\"tex-image\" src\u003d\"CDN_BASE_URL/d6c8ed0de560f88fa572eb1ec2aca1c6?v\u003d1714823840\" style\u003d\"vertical-align: -0.338ex; width:2.325ex; height:2.176ex;\" alt\u003d\"11\"\u003e\u003cspan class\u003d\"tex-text\" style\u003d\"display:none;\"\u003e~11~\u003c/span\u003e\u003c/span\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch4\u003eAdditional Sources\u003c/h4\u003e\n\u003cp\u003eSince the official page does not seem to provide a grader, the following are made available for you to use.\u003c/p\u003e\n\u003cp\u003e\u003ca href\u003d\"https://static.dmoj.ca/data/joi/joi14p1/factories.h\"\u003efactories.h\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003e\u003ca href\u003d\"https://static.dmoj.ca/data/joi/joi14p1/factories.cpp\"\u003efactories.cpp\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003e\u003ca href\u003d\"https://static.dmoj.ca/data/joi/joi14p1/grader.cpp\"\u003egrader.cpp\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003eThe code in \u003ccode\u003efactories.h\u003c/code\u003e includes the prototype functions that you need to implement, but do not write your code in this file.\nThe code in \u003ccode\u003efactories.cpp\u003c/code\u003e includes a sample of the functions you should fill in to solve the problem. You should submit the contents of this file to the judge for grading.\nThe code in \u003ccode\u003egrader.cpp\u003c/code\u003e includes the main function and should be used to run judge your program.\u003c/p\u003e\n\u003cp\u003eIf you are using \u003ccode\u003eg++\u003c/code\u003e, then you can compile the program with \u003ccode\u003eg++ factories.cpp grader.cpp -std\u003dc++11\u003c/code\u003e. If you are using an IDE, then consult Stack Overflow on how to add files into your project.\u003c/p\u003e\n\u003c/div\u003e\n\u003chr\u003e\n\n\u003c/div\u003e"}}]}