Given a string ~S~ of length ~N~ consisting of < and >, generate a permutation ~A~ of the integers ~[1,N+1]~ such that if ~S_i = ~<, ~A_i < A_{i+1}~, otherwise, ~A_i > A_{i+1}~. If there are multiple solutions, print the lexicographically least.

Input Specification

The first line of input will contain the integer ~N\ (1 \leq N \leq 10^6)~, the length of the string. The next line will contain the string ~S~ of length ~N~.

Output Specification

On one line, output the lexicographically least permutation ~A~ that satisfies the requirements.

Subtasks

Subtask 1 [30%]

~N \leq 10^3~

Subtask 2 [70%]

No further constraints.

Sample Input

4
<<><

Sample Output

1 2 4 3 5