{"raw_statement":[{"iden":"problem statement","content":"There are $N$ cities. There are also $K$ roads and $L$ railways, extending between the cities. The $i$\\-th road bidirectionally connects the $p_i$\\-th and $q_i$\\-th cities, and the $i$\\-th railway bidirectionally connects the $r_i$\\-th and $s_i$\\-th cities. No two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.\nWe will say city $A$ and $B$ are _connected by roads_ if city $B$ is reachable from city $A$ by traversing some number of roads. Here, any city is considered to be connected to itself by roads. We will also define _connectivity by railways_ similarly.\nFor each city, find the number of the cities connected to that city by both roads and railways."},{"iden":"constraints","content":"*   $2 ≦ N ≦ 2*10^5$\n*   $1 ≦ K, L≦ 10^5$\n*   $1 ≦ p_i, q_i, r_i, s_i ≦ N$\n*   $p_i < q_i$\n*   $r_i < s_i$\n*   When $i ≠ j$, $(p_i, q_i) ≠ (p_j, q_j)$\n*   When $i ≠ j$, $(r_i, s_i) ≠ (r_j, s_j)$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $K$ $L$\n$p_1$ $q_1$\n:\n$p_K$ $q_K$\n$r_1$ $s_1$\n:\n$r_L$ $s_L$"},{"iden":"sample input 1","content":"4 3 1\n1 2\n2 3\n3 4\n2 3"},{"iden":"sample output 1","content":"1 2 2 1\n\nAll the four cities are connected to each other by roads.\nBy railways, only the second and third cities are connected. Thus, the answers for the cities are $1, 2, 2$ and $1$, respectively."},{"iden":"sample input 2","content":"4 2 2\n1 2\n2 3\n1 4\n2 3"},{"iden":"sample output 2","content":"1 2 2 1"},{"iden":"sample input 3","content":"7 4 4\n1 2\n2 3\n2 5\n6 7\n3 5\n4 5\n3 4\n6 7"},{"iden":"sample output 3","content":"1 1 2 1 2 2 2"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}