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 update(grid, i, j, k):\n used = [0]*6\n # 0 -2 -2 0 -1 1 -1 -1\n if j-2 >= 0:\n  used[grid[i][j-2]] = 1\n if i-2 >= 0:\n  used[grid[i-2][j]] = 1 \n if i-1 >= 0 and j-1 >= 0:\n  used[grid[i-1][j-1]] = 1\n if i-1 >= 0 and j+1 < len(grid[0]):\n  used[grid[i-1][j+1]] = 1\n\n##    print("%d %d" % (i, j))\n##    print(used)\n##    print(grid)\n #return the first available value\n #print("k: %d" % k)\n for fill in range(1,5):\n  if used[fill] == 0:\n   if fill > k:\n    k = fill\n   grid[i][j] = fill\n   return k\n #This shouldn\'t happen\n grid[i][j] = 5\n return 5\n  \n\ngrid5050 = [[0]*50 for row in range(50)]\nk=1\nfor i in range(50):\n for j in range(50):\n  k = update(grid5050, i, j, k)\nnoOfCases = int(input())\nfor case in range(noOfCases):\n #Read in data for each case\n n,m = list(map(int, input().split()))\n #print("N and M %d %d" % (n,m))\n k = 1\n grid = [[0]*m for row in range(n)]\n\n if n>=3 and m>=3:\n  k= 4\n  for i in range(n):\n   for j in range(m):\n    grid[i][j] = grid5050[i][j] \n elif n == 2 and m > 2:\n  #this case i missed??\n  k = 3\n  for j in range(m):\n   next = j % 3 +1\n   grid[0][j] = next\n   grid[1][j] = next\n else:\n  for i in range(n):\n   for j in range(m):\n    k = update(grid, i, j, k)\n \n print(k) \n print((\'\\n\'.join([\'\'.join([(str(item)+\' \') for item in row]) \n  for row in grid]))) \n        \n  \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 37627