{"problem":{"name":"Distance Pairs","description":{"content":"There is an undirected connected graph with $N$ vertices numbered $1$ through $N$. The lengths of all edges in this graph are $1$. It is known that for each $i (1≦i≦N)$, the distance between vertex $1","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"codefestival_2016_ex_a"},"statements":[{"statement_type":"Markdown","content":"There is an undirected connected graph with $N$ vertices numbered $1$ through $N$. The lengths of all edges in this graph are $1$. It is known that for each $i (1≦i≦N)$, the distance between vertex $1$ and vertex $i$ is $A_i$, and the distance between vertex $2$ and vertex $i$ is $B_i$. Determine whether there exists such a graph. If it exists, find the minimum possible number of edges in it.\n\n## Constraints\n\n*   $2≦N≦10^5$\n*   $0≦A_i,B_i≦N-1$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $B_1$\n$A_2$ $B_2$\n:\n$A_N$ $B_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"codefestival_2016_ex_a","tags":[],"sample_group":[["4\n0 1\n1 0\n1 1\n2 1","4\n\nThe figure below shows two possible graphs. The graph on the right has fewer edges.\n![image](https://atcoder.jp/img/code-festival-2016-final/dd1e04d837fd7fc1be56b231cd8c2a17.png)"],["3\n0 1\n1 0\n2 2","\\-1\n\nSuch a graph does not exist."]],"created_at":"2026-03-03 11:01:14"}}