B. Inequalities
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There are 2*N+1 empty cards in a row. Petya writes the sign ">" or "<" on each even card at his discretion. Will Vasya be able to write numbers from 1 to (N+1) on odd cards so that all inequalities are true? Each number must be written exactly once.

Input

The first line contains a natural number N ($$$N\le10^5$$$). The second line contains a sequence of N signs ">" and "<", separated by spaces.

Output

Output a sequence of natural numbers separated by spaces, which solves Vasya's problem if possible, otherwise output -1.

Example
Input
2
< >
Output
1 3 2