{"problem":{"name":"Equals","description":{"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 $(x_1,y_1)$, $(x_2,y_2)$, ..","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc097_b"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $2$ $≤$ $N$ $≤$ $10^5$\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.\n\n## Input\n\nInput 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$x_M$ $y_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc097_b","tags":[],"sample_group":[["5 2\n5 3 1 4 2\n1 3\n5 4","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 $2$."],["3 2\n3 2 1\n1 2\n2 3","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."],["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","8"],["5 1\n1 2 3 4 5\n1 5","5\n\nWe do not have to perform the operation."]],"created_at":"2026-03-03 11:01:14"}}