Little Z has recently become obsessed with jigsaw puzzles, but his intelligence is limited, and he is never able to complete a puzzle. The game is as follows: First, Little Z receives some puzzle pieces, and then he tries to rearrange these pieces to form a $4 \times 4$ square. See the figure below. Note that Little Z cannot rotate or flip these pieces.

Figure 1: Picture 1

Figure 2: Picture 2

Little Z receives the pieces shown in Figure 1 and then rearranges them to obtain the square in Figure 2. Since Little Z is too slow, please write a program to help him solve this problem.

Input

The input contains multiple test cases. Please use EOF to terminate.

The first line of each test case contains a single integer $N$, the number of pieces. Then $N$ pieces follow. The first line of each piece contains two integers $r$ and $c$, representing the number of rows and columns of the piece. Then $r$ lines follow, each containing $c$ characters '0' or '1'. '1' indicates that the piece occupies this position, and '0' indicates that this position is empty. It is guaranteed that each piece is a complete piece (i.e., the '1's are connected) and there are no empty rows or columns.

Output

If it is impossible to form a square, output "No solution". If there are multiple solutions, output "Yes, many!". Otherwise, output "Yes, only one!", and then output the $4 \times 4$ matrix $H$, where $H_{ij}$ represents the piece number at position $i, j$. Piece numbers start from 1.

Examples

Input 1

4
2 3
111
101
4 2
01
01
11
01
2 1
1
1
3 2
10
10
11
4
1 4
1111
1 4
1111
1 4
1111
1 4
1111
4
1 4
1111
1 4
1111
1 4
1111
2 3
111
001

Output 1

Yes, only one!
1112
1412
3422
3442
Yes, many!
No solution

Constraints

For 30% of the data, $N < 5$. For 100% of the data, $N \leq 16$.