Description

There are N nodes in the graph. Given the length of edges between the nodes, find the shortest path of size N and the nodes in the path are all different.

Input Format

First line: one positive integer N (N <= 15).
Next N lines: the i-th line contains N non-negative integers (<= 1000) indicating the length of edges between the i-th node and other nodes.

Output Format

One line contains N integers, indicating the indexes of nodes in the shortest path.

4
0 2 8 4
2 0 5 7
8 5 0 1
4 7 1 0

3 4 1 2