VNOI Marathon 08

The VM08 arena

In this year Marathon '08, the vCoders have to play in a knock-out tournament. After the qualification round, the board of directors has selected N competitors of highest scores and numbered them from 1 to N. These competitors have to stand in order along a circle (so that the n^th person is beside the first one). Then the board selects a random two ajdacent competitors to compete with each other. The loser is eliminated and has to go out of the circle. The tournament continues in this way until there is only one competitor left. This competitor will be the ultimate champion.

Knowing in advance the winners in all matches, help the board to determine who have chance to be the champion.

Input

• The first line: an integer N (3 ≤ N ≤ 500).
• In the next N lines there is a matrix A[i, j], in which A[i, j] = 0 if the i^th competitor will lose over the j^th competitor and A[i, j] = 1 if the i^th competitor will win over the j^th competitor. It is guaranteed that A[i, i] = 1 for all i and A[i, j] + A[j, i] = 1 for i <> j. The numbers are separated by at least one space.

Output

• The first line: a positive integer M - the number of competitors that have chance to be the champion.
• In each line in the next M lines, print M numbers that are the indexes of the competitors that have chance to be the champion. The indexes should be printed in ascending order.

Example

Input
7
1 1 1 1 1 0 1
0 1 0 1 1 0 0
0 1 1 1 1 1 1
0 0 0 1 1 0 1
0 0 0 0 1 0 1
1 1 0 1 1 1 1
0 1 0 0 0 0 1

Output
3
1
3
6