Cycle

A graph is given. Determine does it contain a cycle of negative weight, and if so, print it.

Input

The first line contains the number of vertices n (1 ≤ n ≤ 100). Each of the next n lines contains n numbers - the adjacency matrix of the graph. Weights of the edges do not exceed 10000 by absolute value. If the edge is absent, the corresponding value is 100000.

Output

Print in the first line "YES", if a cycle exists, or "NO" otherwise. In the presence of the cycle output in the second row the number of vertices in it (assuming the same first and last) and the third row - tops included in this series in order of traversal. If several cycles - output any.

Examples