{"raw_statement":[{"iden":"problem statement","content":"Given is a tree with $N$ vertices. The vertices are numbered $1,2,\\ldots,N$, and the $i$\\-th edge $(1 \\leq i \\leq N-1)$ connects Vertex $u_i$ and Vertex $v_i$.\nFind the number of integers $i$ $(1 \\leq i \\leq N)$ that satisfy the following condition.\n\n*   The size of the maximum matching of the graph obtained by deleting Vertex $i$ and all incident edges from the tree is equal to the size of the maximum matching of the original tree."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq u_i < v_i \\leq N$\n*   The given graph is a tree.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$\n$u_1$ $v_1$\n$u_2$ $v_2$\n$\\vdots$\n$u_{N-1}$ $v_{N-1}$"},{"iden":"sample input 1","content":"3\n1 2\n2 3"},{"iden":"sample output 1","content":"2\n\nThe size of the maximum matching of the original tree is $1$.\nThe size of the maximum matching of the graph obtained by deleting Vertex $1$ and all incident edges from the tree is $1$.\nThe size of the maximum matching of the graph obtained by deleting Vertex $2$ and all incident edges from the tree is $0$.\nThe size of the maximum matching of the graph obtained by deleting Vertex $3$ and all incident edges from the tree is $1$.\nThus, two integers $i=1,3$ satisfy the condition, so we should print $2$."},{"iden":"sample input 2","content":"2\n1 2"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"6\n2 5\n3 5\n1 4\n4 5\n4 6"},{"iden":"sample output 3","content":"4"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}