{"problem":{"name":"Lucky 7 Battle","description":{"content":"We have a string $S$ of length $N$ consisting of `0`, $\\ldots$, `9`, and a string $X$ of length $N$ consisting of `A` and `T`. Additionally, there is a string $T$, which is initialized to an empty str","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc195_e"},"statements":[{"statement_type":"Markdown","content":"We have a string $S$ of length $N$ consisting of `0`, $\\ldots$, `9`, and a string $X$ of length $N$ consisting of `A` and `T`. Additionally, there is a string $T$, which is initialized to an empty string.\nTakahashi and Aoki will play a game using these. The game consists of $N$ rounds. In the $i$\\-th round $(1\\leq i \\leq N)$, the following happens:\n\n*   If $X_i$ is `A`, Aoki does the operation below; if $X_i$ is `T`, Takahashi does it.\n*   Operation: append $S_i$ or `0` at the end of $T$.\n\nAfter $N$ operations, $T$ will be a string of length $N$ consisting of `0`, $\\ldots$, `9`. If $T$ is a multiple of $7$ as a base-ten number (after removing leading zeros), Takahashi wins; otherwise, Aoki wins.\nDetermine the winner of the game when the two players play optimally.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2\\times 10^5$\n*   $S$ and $X$ have a length of $N$ each.\n*   $S$ consists of `0`, $\\ldots$, `9`.\n*   $X$ consists of `A` and `T`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$S$\n$X$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc195_e","tags":[],"sample_group":[["2\n35\nAT","Takahashi\n\nIn the $1$\\-st round, Aoki appends `3` or `0` at the end of $T$. In the $2$\\-nd round, Takahashi appends `5` or `0` at the end of $T$.\nIf Aoki appends `3`, Takahashi can append `5` to make $T$ `35`, a multiple of $7$.\nIf Aoki appends `0`, Takahashi can append `0` to make $T$ `00`, a multiple of $7$.\nThus, Takahashi can always win."],["5\n12345\nAAAAT","Aoki"],["5\n67890\nTTTTA","Takahashi"],["5\n12345\nATATA","Aoki"]],"created_at":"2026-03-03 11:01:14"}}