>< again

AtCoder

IDagc053_a

Time2000ms

Memory256MB

Difficulty—

We have a string $S$ of length $N$, where each character is `<` or `>`. A non-negative integer sequence of $N+1$ elements, $X_0,X_1,\ldots,X_N$, is said to be _good_ when it satisfies the following for every $1 \leq i \leq N$: * $X_{i-1}<X_i$, if $S_i$ is `<`; * $X_{i-1}>X_i$, if $S_i$ is `>`. Given a good non-negative integer sequence $A$, divide it into as many good non-negative integer sequences as possible. That is, find a positive integer $k$ and $k$ good non-negative integer sequences $B_1,B_2,\ldots, B_k$ satisfying the following with the maximum possible value of $k$: * For every $0 \leq i \leq N$, the sum of the $i$\-th elements of $B_1,\ldots,B_k$ equals $A_i$. ## Constraints * $1 \leq N \leq 100$ * $0 \leq A_i \leq 10^4$ * $S$ is a string of length $N$ consisting of `<` and `>`. * $A$ is a good non-negative integer sequence. Particularly, $A$ has $N+1$ elements. ## Input Input is given from Standard Input in the following format: $N$ $S$ $A_0$ $A_1$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3
<><
3 8 6 10

Output #1

2
1 5 4 7
2 3 2 3

API Response (JSON)

{
  "problem": {
    "name": ">< again",
    "description": {
      "content": "We have a string $S$ of length $N$, where each character is `<` or `>`. A non-negative integer sequence of $N+1$ elements, $X_0,X_1,\\ldots,X_N$, is said to be _good_ when it satisfies the following fo",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc053_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a string $S$ of length $N$, where each character is `<` or `>`.\nA non-negative integer sequence of $N+1$ elements, $X_0,X_1,\\ldots,X_N$, is said to be _good_ when it satisfies the following fo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments