Permutation

AtCoder

IDdp_t

Time2000ms

Memory256MB

Difficulty—

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 the following condition, modulo $10^9 + 7$: * 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 `>`. ## Constraints * $N$ is an integer. * $2 \leq N \leq 3000$ * $s$ is a string of length $N - 1$. * $s$ consists of `<` and `>`. ## Input Input is given from Standard Input in the following format: $N$ $s$ [samples]

Samples

Input #1

4
<><

Output #1

5

There are five permutations that satisfy the condition, as follows:

*   $(1, 3, 2, 4)$
*   $(1, 4, 2, 3)$
*   $(2, 3, 1, 4)$
*   $(2, 4, 1, 3)$
*   $(3, 4, 1, 2)$

Input #2

5
<<<<

Output #2

1

There is one permutation that satisfies the condition, as follows:

*   $(1, 2, 3, 4, 5)$

Input #3

20
>>>><>>><>><>>><<>>

Output #3

217136290

Be sure to print the number modulo $10^9 + 7$.

API Response (JSON)

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    "name": "Permutation",
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      "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",
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      "memory_limit": 262144
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    "is_sync": true,
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      "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 th...",
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