{"raw_statement":[{"iden":"problem statement","content":"We have a permutation of the integers from $1$ through $N$, $p_1$, $p_2$, .., $p_N$. We also have $M$ pairs of two integers between $1$ and $N$ (inclusive), represented as $(x_1,y_1)$, $(x_2,y_2)$, .., $(x_M,y_M)$. AtCoDeer the deer is going to perform the following operation on $p$ as many times as desired so that the number of $i$ ($1$ $≤$ $i$ $≤$ $N$) such that $p_i = i$ is maximized:\n\n*   Choose $j$ such that $1$ $≤$ $j$ $≤$ $M$, and swap $p_{x_j}$ and $p_{y_j}$.\n\nFind the maximum possible number of $i$ such that $p_i = i$ after operations."},{"iden":"constraints","content":"*   $2$ $≤$ $N$ $≤$ $10^5$\n*   $1$ $≤$ $M$ $≤$ $10^5$\n*   $p$ is a permutation of integers from $1$ through $N$.\n*   $1$ $≤$ $x_j,y_j$ $≤$ $N$\n*   $x_j$ $≠$ $y_j$\n*   If $i$ $≠$ $j$, ${x_i,y_i}$ $≠$ ${x_j,y_j}$.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$p_1$ $p_2$ $..$ $p_N$\n$x_1$ $y_1$\n$x_2$ $y_2$\n$:$\n$x_M$ $y_M$"},{"iden":"sample input 1","content":"5 2\n5 3 1 4 2\n1 3\n5 4"},{"iden":"sample output 1","content":"2\n\nIf we perform the operation by choosing $j=1$, $p$ becomes `1 3 5 4 2`, which is optimal, so the answer is $2$."},{"iden":"sample input 2","content":"3 2\n3 2 1\n1 2\n2 3"},{"iden":"sample output 2","content":"3\n\nIf we perform the operation by, for example, choosing $j=1$, $j=2$, $j=1$ in this order, $p$ becomes `1 2 3`, which is obviously optimal. Note that we may choose the same $j$ any number of times."},{"iden":"sample input 3","content":"10 8\n5 3 6 8 7 10 9 1 2 4\n3 1\n4 1\n5 9\n2 5\n6 5\n3 5\n8 9\n7 9"},{"iden":"sample output 3","content":"8"},{"iden":"sample input 4","content":"5 1\n1 2 3 4 5\n1 5"},{"iden":"sample output 4","content":"5\n\nWe do not have to perform the operation."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}