You are given an empty grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). You should fill this grid with integers in a way that satisfies the following rules:
- For any three cells $c_1$, $c_2$ and $c_3$ such that $c_1$ shares a side with $c_2$ and another side with $c_3$, the integers written in cells $c_2$ and $c_3$ are distinct.
- Let's denote the number of different integers in the grid by $K$; then, each of these integers should lie between $1$ and $K$ inclusive.
- $K$ should be minimum possible.
Find the minimum value of $K$ and a resulting (filled) grid. If there are multiple solutions, you may find any one.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains two space-separated integers $N$ and $M$.

-----Output-----
- For each test case, print $N+1$ lines.
- The first line should contain a single integer — the minimum $K$.
- Each of the following $N$ lines should contain $M$ space-separated integers between $1$ and $K$ inclusive. For each valid $i, j$, the $j$-th integer on the $i$-th line should denote the number in the $i$-th row and $j$-th column of the grid.

-----Constraints-----
- $1 \le T \le 500$
- $1 \le N, M \le 50$
- the sum of $N \cdot M$ over all test cases does not exceed $7 \cdot 10^5$

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
2
1 1
2 3

-----Example Output-----
1
1
3
1 1 2
2 3 3

-----Explanation-----
Example case 1: There is only one cell in the grid, so the only valid way to fill it is to write $1$ in this cell. Note that we cannot use any other integer than $1$.
Example case 2: For example, the integers written in the neighbours of cell $(2, 2)$ are $1$, $2$ and $3$; all these numbers are pairwise distinct and the integer written inside the cell $(2, 2)$ does not matter. Note that there are pairs of neighbouring cells with the same integer written in them, but this is OK.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def valid(x,y,m,n):\n if 0<=x<m and 0<=y<n:\n  return 1\n return 0\ndef neigh(A,x,y,m,n):\n B=[]\n if valid(x,y-2,m,n):\n  B.append(A[x][y-2])\n if valid(x-2,y,m,n):\n  B.append(A[x-2][y])\n if valid(x-1,y-1,m,n):\n  B.append(A[x-1][y-1])\n if valid(x-1,y+1,m,n):\n  B.append(A[x-1][y+1])\n return set(B)\n \nAA=[[1,1,2,2],[1,1,2,3],[1,2,2,3],[1,2,3,3],[1,2,2,1],[1,2,3,1],[1,2,3,4]]\nt=int(input())\nfor i in range(t):\n m,n=map(int,input().split())\n if m>=3 and n>=3:\n  P=set(range(1,5))\n elif m==1 and n==1:\n  P=set(range(1,2))\n elif m+n==3:\n  P=set(range(1,2))\n elif m==1 or n==1:\n  P=set(range(1,3))\n elif m==2 and n==2:\n  P=set(range(1,3))\n elif m==2 or n==2:\n  P=set(range(1,4))\n A=[[0 for j in range(n)] for k in range(m)]\n pk=0\n if m==1:\n  A[0][0]=1\n  for j in range(1,n):\n   B=neigh(A,0,j,m,n)\n   A[0][j]=min(P-B)\n  print(max(P))\n  for j in A[0]:\n   print(j,end=" ")\n  print()\n  continue\n while True:\n  trig=0\n  if max(P)==4:\n   for j in range(n):\n    A[0][j]=AA[pk][j%4]\n  else:\n   for j in range(n):\n    A[0][j]=(j%max(P))+1\n  for j in range(1,m):\n   for k in range(n):\n    B=neigh(A,j,k,m,n)\n    if P-B==set():\n     trig=1\n     break\n    A[j][k]=min(P-B)\n   if trig==1:\n    pk+=1\n    A=[[0 for j in range(n)] for k in range(m)]\n    break\n  else:\n   break\n print(max(P))\n for j in A:\n  for k in j:\n   print(k,end=" ")\n  print()\n   \n   \n \n \n  \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15247