Problem: You are given a matrix a consisting of positive integers. It has n rows and m columns.

Construct a matrix b consisting of positive integers. It should have the same size as a, and the following conditions should be met: 

  * 1 ≤ b_{i,j} ≤ 10^6; 
  * b_{i,j} is a multiple of a_{i,j}; 
  * the absolute value of the difference between numbers in any adjacent pair of cells (two cells that share the same side) in b is equal to k^4 for some integer k ≥ 1 (k is not necessarily the same for all pairs, it is own for each pair). 



We can show that the answer always exists.

Input

The first line contains two integers n and m (2 ≤ n,m ≤ 500).

Each of the following n lines contains m integers. The j-th integer in the i-th line is a_{i,j} (1 ≤ a_{i,j} ≤ 16).

Output

The output should contain n lines each containing m integers. The j-th integer in the i-th line should be b_{i,j}.

Examples

Input


2 2
1 2
2 3


Output


1 2
2 3


Input


2 3
16 16 16
16 16 16


Output


16 32 48
32 48 64


Input


2 2
3 11
12 8


Output


327 583
408 664

Note

In the first example, the matrix a can be used as the matrix b, because the absolute value of the difference between numbers in any adjacent pair of cells is 1 = 1^4.

In the third example: 

  * 327 is a multiple of 3, 583 is a multiple of 11, 408 is a multiple of 12, 664 is a multiple of 8; 
  * |408 - 327| = 3^4, |583 - 327| = 4^4, |664 - 408| = 4^4, |664 - 583| = 3^4. 

Solution (in CPP):

Solution:
#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cstring>
#include<vector>
using namespace std;
typedef long long LL;
const int N=505;
int n,m;
int a[N][N];
int b[N][N];
int d[N];
bool in[1000005];
int main()
{
	memset(in,false,sizeof(in));
	for (int u=1;u<=16;u++) 
	{
		d[u]=u*u*u*u;
		in[d[u]]=true;
	}
	scanf("%d%d",&n,&m);
	for (int u=1;u<=n;u++)
	for (int i=1;i<=m;i++)
	scanf("%d",&a[u][i]);
	for (int u=1;u<=n;u++)
	{
		for (int i=1;i<=m;i++)
		{
			if ((u+i)&1) printf("720720 ");
			else printf("%d ",720720-d[a[u][i]]);
		}
		printf("\n");
	}
	return 0;
}