{"problem":{"name":"TTPC Never Ends","description":{"content":"The abbreviation-deciding machine $\\mathrm{M}$ for a programming contest has a string $S$ of length $N$ consisting of uppercase English letters and an integer sequence $A = (A_1, A_2, \\dots, A_N)$ of ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"ttpc2024_2_h"},"statements":[{"statement_type":"Markdown","content":"The abbreviation-deciding machine $\\mathrm{M}$ for a programming contest has a string $S$ of length $N$ consisting of uppercase English letters and an integer sequence $A = (A_1, A_2, \\dots, A_N)$ of length $N$.  \nAdditionally, machine $\\mathrm{M}$ has four cursors numbered from $1$ to $4$ for pointing at characters in $S$. Initially, for each $i = 1, 2, 3, 4$, cursor $i$ points to the $x_i$\\-th character of $S$.\nThe machine $\\mathrm{M}$ has two buttons: the **Abbreviation Button** and the **Update Button**. Pressing these buttons triggers the following actions:\n\n*   **Abbreviation Button**: Machine $\\mathrm{M}$ outputs a string of length $4$ formed by concatenating the characters pointed to by cursors $1, 2, 3, 4$ in this order.\n*   **Update Button**: For each $i = 1, 2, 3, 4$, the following happens:\n    *   Let $y$ be the current position of cursor $i$. Cursor $i$ moves from the $y$\\-th character of $S$ to the $A_y$\\-th character of $S$.\n\nThis year's programming contest abbreviation was determined by pressing the Abbreviation Button, resulting in `TTPC`. Here, \"this year\" refers to $0$ years from now.\nStarting from next year, the abbreviation for the programming contest each year will be obtained through the following steps:\n\n1.  Press the update button.\n2.  Press the abbreviation button to determine the abbreviation.\n\nHow many years from now will the abbreviation return to `TTPC` for the last time? Will the end of `TTPC` come?\n\n## Constraints\n\n*   $N, A_i, x_1, x_2, x_3, x_4$ are integers.\n*   $3 \\leq N \\leq 50$\n*   $S$ is a string of length $N$ consisting of uppercase English letters.\n*   $1 \\leq A_i \\leq N\\ (1 \\leq i \\leq N)$\n*   $1 \\leq x_1, x_2, x_3, x_4 \\leq N$\n*   $S_{x_1} = {}$`T`\n*   $S_{x_2} = {}$`T`\n*   $S_{x_3} = {}$`P`\n*   $S_{x_4} = {}$`C`\n\n## Input\n\nThe input is given in the following format:\n\n$N$\n$S$\n$A_1$ $A_2$ $\\dots$ $A_N$\n$x_1$ $x_2$ $x_3$ $x_4$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"ttpc2024_2_h","tags":[],"sample_group":[["5\nTTTPC\n2 3 4 4 5\n1 2 4 5","1\n\n*   $0$ years from now, the abbreviation is `TTPC`, and the cursor positions are $(1,2,4,5)$.\n*   $1$ year from now, the abbreviation is `TTPC`, and the cursor positions are $(2,3,4,5)$.\n*   $2$ years from now, the abbreviation is `TPPC`, and the cursor positions are $(3,4,4,5)$.\n*   $3$ years from now, the abbreviation is `PPPC`, and the cursor positions are $(4,4,4,5)$.\n\nThe last time the abbreviation becomes `TTPC` is 1 year from now."],["4\nTTPC\n2 3 4 1\n1 2 3 4","NeverEnds\n\nThe abbreviation becomes `TTPC` at years $0, 4, 8, 12, \\dots$ and so on. `TTPC` never ends."],["6\nTTPCZT\n5 3 2 6 4 4\n1 2 3 4","0"]],"created_at":"2026-03-03 11:01:14"}}