{"trustable":false,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"MD","content":"有一棵由 n 个顶点组成的无根树。\n\n现在需要将这棵树分解成多条**不重边**的路径(一条路径 由多条边连通而成,没有分支; 每条边归属且只归属于一条路径),且要求 每条路径与其余路径至少有一个公共端点(是端点不是交点)。\n\n请判断给定的树是否可以成功分解,如果可以分解,请给出具体方案。如果有多种答案,可输出任意一种。"}},{"title":"Input","value":{"format":"MD","content":"第一行一个整数 n ( 2 \u0026le; n \u0026le; 100000) 表示树的顶点数。\n\n之后 n-1 行,每行两个整数 u 和 v,表示 u 和 v之间有一条边。"}},{"title":"Output","value":{"format":"MD","content":"如果不能成功分解,输出一行 No。\n\n否则:\n\n第一行输出 Yes。之后输出一行一个整数 m,表示分解出的路径数量。\n\n之后 m 行, 每行两个顶点 u\u003csub\u003ei\u003c/sub\u003e , v\u003csub\u003ei\u003c/sub\u003e (1 \u0026le; u\u003csub\u003ei\u003c/sub\u003e, v\u003csub\u003ei\u003c/sub\u003e \u0026le; n, u\u003csub\u003ei\u003c/sub\u003e \u0026ne; v\u003csub\u003ei\u003c/sub\u003e ),表示分解出的路径的两个端点。\n\n对于所有 path(u\u003csub\u003ei\u003c/sub\u003e , v\u003csub\u003ei\u003c/sub\u003e ) 和 path(u\u003csub\u003ej\u003c/sub\u003e , v\u003csub\u003ej\u003c/sub\u003e ) 必须满足 u\u003csub\u003ei\u003c/sub\u003e \u003d u\u003csub\u003ej\u003c/sub\u003e || u\u003csub\u003ei\u003c/sub\u003e \u003d v\u003csub\u003ej\u003c/sub\u003e || v\u003csub\u003ei\u003c/sub\u003e \u003d u\u003csub\u003ej\u003c/sub\u003e || v\u003csub\u003ei\u003c/sub\u003e \u003d v\u003csub\u003ej\u003c/sub\u003e。"}},{"title":"Examples","value":{"format":"MD","content":"\u003cdiv class\u003d\"sample-test\"\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e4\u003cbr\u003e1 2\u003cbr\u003e2 3\u003cbr\u003e3 4\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003eYes\u003cbr\u003e1\u003cbr\u003e1 4\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e6\u003cbr\u003e1 2\u003cbr\u003e2 3\u003cbr\u003e3 4\u003cbr\u003e2 5\u003cbr\u003e3 6\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003eNo\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e5\u003cbr\u003e1 2\u003cbr\u003e1 3\u003cbr\u003e1 4\u003cbr\u003e1 5\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003eYes\u003cbr\u003e4\u003cbr\u003e1 2\u003cbr\u003e1 3\u003cbr\u003e1 4\u003cbr\u003e1 5\u003cbr\u003e\u003c/pre\u003e\n \u003c/div\u003e\n\u003c/div\u003e"}},{"title":"Note","value":{"format":"MD","content":"\u003cp\u003eThe tree from the first example is shown on the picture below: \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/b8f5881ed06332f005f8a31f229e4a2b?v\u003d1621240711\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e The number next to each edge corresponds to the path number in the decomposition. It is easy to see that this decomposition suits the required conditions.\u003c/p\u003e\n\u003cp\u003eThe tree from the second example is shown on the picture below: \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/84b1f8263ccc284a6d734e536b4d6f2e?v\u003d1621240711\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e We can show that there are no valid decompositions of this tree.\u003c/p\u003e\n\u003cp\u003eThe tree from the third example is shown on the picture below: \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/96ce0d9c8a70bce04fba5efdeda7e299?v\u003d1621240711\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e The number next to each edge corresponds to the path number in the decomposition. It is easy to see that this decomposition suits the required conditions.\u003c/p\u003e"}}]}