For an $n \times m$ binary matrix $A$ and an $m \times p$ binary matrix $B$, their product is defined as an $n \times p$ binary matrix $C$, where $C_{i,j} = \bigoplus_{k=1}^{m} A_{i,k} \& B_{k,j}$ $^\dagger$.

Now, Link wants to perform the inverse operation of multiplication—division. Given an $n \times m$ binary matrix $A$ and an $n \times p$ binary matrix $C$, you need to find an $m \times p$ matrix $B$ such that the product of $A$ and $B$ is exactly equal to $C$.

$^\dagger$ $\oplus$ denotes the bitwise XOR operation, and $\&$ denotes the bitwise AND operation. For example: $(0011)_2 \oplus (0101)_2 = (0110)_2$, $(0011)_2 \& (0101)_2 = (0001)_2$.

Input

Each test file contains only one test case.

The first line contains three integers $n, m, p$ ($1 \le n, m, p \le 1000$).

The next $n$ lines, the $i$-th line contains $m$ integers $A_{i,1}, A_{i,2}, \dots, A_{i,m}$ ($A_{i,j} \in \{0, 1\}$), representing the elements of matrix $A$.

The next $n$ lines, the $i$-th line contains $p$ integers $C_{i,1}, C_{i,2}, \dots, C_{i,p}$ ($C_{i,j} \in \{0, 1\}$), representing the elements of matrix $C$.

Output

If no matrix $B$ satisfies the condition, output "No".

If there exists a matrix $B$ that satisfies the condition, output "Yes" on the first line, followed by $m$ lines, each containing $p$ integers $B_{i,1}, B_{i,2}, \dots, B_{i,p}$ ($B_{i,j} \in \{0, 1\}$), representing the matrix $B$ you found.

If there are multiple matrices $B$ that satisfy the condition, you may output any one of them.

Examples

Input 1

3 2 3
1 0
1 1
1 0
0 0 0
0 1 0
0 0 0

Output 1

Yes
0 0 0
0 1 0

Input 2

3 2 3
1 0
1 1
1 0
1 0 0
0 1 0
0 0 1

Output 2

No