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

Print your answer to Standard Output in the following format:

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

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