{"problem":{"name":"Permutation","description":{"content":"Let $N$ be a positive integer. You are given a string $s$ of length $N - 1$, consisting of `<` and `>`. Find the number of permutations $(p_1, p_2, \\ldots, p_N)$ of $(1, 2, \\ldots, N)$ that satisfy th","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"dp_t"},"statements":[{"statement_type":"Markdown","content":"Let $N$ be a positive integer. You are given a string $s$ of length $N - 1$, consisting of `<` and `>`.\nFind the number of permutations $(p_1, p_2, \\ldots, p_N)$ of $(1, 2, \\ldots, N)$ that satisfy the following condition, modulo $10^9 + 7$:\n\n*   For each $i$ ($1 \\leq i \\leq N - 1$), $p_i < p_{i + 1}$ if the $i$\\-th character in $s$ is `<`, and $p_i > p_{i + 1}$ if the $i$\\-th character in $s$ is `>`.\n\n## Constraints\n\n*   $N$ is an integer.\n*   $2 \\leq N \\leq 3000$\n*   $s$ is a string of length $N - 1$.\n*   $s$ consists of `<` and `>`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$s$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"dp_t","tags":[],"sample_group":[["4\n<><","5\n\nThere are five permutations that satisfy the condition, as follows:\n\n*   $(1, 3, 2, 4)$\n*   $(1, 4, 2, 3)$\n*   $(2, 3, 1, 4)$\n*   $(2, 4, 1, 3)$\n*   $(3, 4, 1, 2)$"],["5\n<<<<","1\n\nThere is one permutation that satisfies the condition, as follows:\n\n*   $(1, 2, 3, 4, 5)$"],["20\n>>>><>>><>><>>><<>>","217136290\n\nBe sure to print the number modulo $10^9 + 7$."]],"created_at":"2026-03-03 11:01:14"}}