Cycle

Input

The first line contains the number of vertices $n$ (1 \le n \le 100). Each of the next $n$ lines contains $n$ numbers—the adjacency matrix of the graph. The weights of the edges do not exceed $10000$ in absolute value. If an edge is absent, the corresponding value is $100000$.

Output

If a negative weight cycle exists, print "YES" in the first line; otherwise, print "NO". If a cycle exists, output in the second line the number of vertices in it (counting the same first and last vertices), and in the third line, output the vertices included in this cycle in order of traversal. If multiple such cycles exist, output any one of them.

Examples