Contest Duration: - (local time) (180 minutes) Back to Home
A - >< again /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• S_i< のとき : X_{i-1}<X_i
• S_i > のとき : X_{i-1}>X_i

• すべての 0 \leq i \leq N について B_1,\ldots,B_ki 項目の値の合計は A_i と等しい。

### 制約

• 1 \leq N \leq 100
• 0 \leq A_i \leq 10^4
• S<> からなる長さ N の文字列である。
• A は良い非負整数列である。特に、要素数は N+1 である。

### 入力

N
S
A_0 A_1 \cdots A_N


### 出力

k
B_{1,0} B_{1,1} \cdots B_{1,N}
:
B_{k,0} B_{k,1} \cdots B_{k,N}


ここで、B_{i,j} は良い非負整数列 B_ij 項目の値を表している。

### 入力例 1

3
<><
3 8 6 10


### 出力例 1

2
1 5 4 7
2 3 2 3


Score : 400 points

### Problem Statement

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


### Output

k
B_{1,0} B_{1,1} \cdots B_{1,N}
:
B_{k,0} B_{k,1} \cdots B_{k,N}


Here, B_{i,j} denotes the value of the j-th element of the good non-negative integer sequence B_i.

### Sample Input 1

3
<><
3 8 6 10


### Sample Output 1

2
1 5 4 7
2 3 2 3