Cycle

Input

The first line contains the integer $n$ (1 \le n \le 250), the number of vertices in the graph. The following $n$ lines each contain $n$ integers, representing the adjacency matrix of the graph. The weight of each edge does not exceed $10000$ in absolute value. If there is no edge between two vertices, the corresponding entry in the matrix is $1000000000$.

Vertices are numbered from $1$ to $n$.

Output

On the first line, output YES if a negative weight cycle exists in the graph, or NO otherwise. If a negative cycle exists, on the second line, output the number of vertices in the cycle (including the repeated start/end vertex), and on the third line, output the indices of the vertices in the order they appear in the cycle.

Examples