{"problem":{"name":"Three Variables Game","description":{"content":"There is a game that involves three variables, denoted $A$, $B$, and $C$. As the game progresses, there will be $N$ events where you are asked to make a choice. Each of these choices is represented by","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc166_f"},"statements":[{"statement_type":"Markdown","content":"There is a game that involves three variables, denoted $A$, $B$, and $C$.\nAs the game progresses, there will be $N$ events where you are asked to make a choice. Each of these choices is represented by a string $s_i$. If $s_i$ is `AB`, you must add $1$ to $A$ or $B$ then subtract $1$ from the other; if $s_i$ is `AC`, you must add $1$ to $A$ or $C$ then subtract $1$ from the other; if $s_i$ is `BC`, you must add $1$ to $B$ or $C$ then subtract $1$ from the other.\nAfter each choice, none of $A$, $B$, and $C$ should be negative.\nDetermine whether it is possible to make $N$ choices under this condition. If it is possible, also give one such way to make the choices.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^5$\n*   $0 \\leq A,B,C \\leq 10^9$\n*   $N, A, B, C$ are integers.\n*   $s_i$ is `AB`, `AC`, or `BC`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $A$ $B$ $C$\n$s_1$\n$s_2$\n$:$\n$s_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc166_f","tags":[],"sample_group":[["2 1 3 0\nAB\nAC","Yes\nA\nC\n\nYou can successfully make two choices, as follows:\n\n*   In the first choice, add $1$ to $A$ and subtract $1$ from $B$. $A$ becomes $2$, and $B$ becomes $2$.\n*   In the second choice, add $1$ to $C$ and subtract $1$ from $A$. $C$ becomes $1$, and $A$ becomes $1$."],["3 1 0 0\nAB\nBC\nAB","No"],["1 0 9 0\nAC","No"],["8 6 9 1\nAC\nBC\nAB\nBC\nAC\nBC\nAB\nAB","Yes\nC\nB\nB\nC\nC\nB\nA\nA"]],"created_at":"2026-03-03 11:01:14"}}