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 = 'for _ in range(int(input())):\n row, col = map(int, input().split())\n if row == 1 and col == 1:\n  print("1\\n1")\n\n elif row == 1:\n  if col > 2:\n   print(2)\n  else:\n   print(1)\n  ls = [1, 1, 2, 2]\n  for i in range(col):\n   print(ls[i%4], end=\' \')\n  print()\n\n elif col == 1:\n  if row > 2:\n   print(2)\n  else:\n   print(1)\n  ls = [1, 1, 2, 2]\n  for i in range(row):\n   print(ls[i%4])\n\n elif col == 2:\n  if row == 2:\n   print("2\\n1 2\\n1 2")\n  else:\n   print(3)\n   for j in range(row):\n    for i in range(col):\n     print((j%3)+1, end=\' \')\n    print()\n\n elif row == 2:\n  if col == 2:\n   print("2\\n1 2\\n1 2")\n\n  else:\n   print(3)\n   for j in range(2):\n    for i in range(col):\n     print((i%3)+1, end=\' \')\n    print() \n\n else:\n  first = [1, 1, 2, 2]\n  second = [2, 2, 1, 1]\n  third = [3, 3, 4, 4]\n  fourth = [4, 4, 3, 3]\n  first_found = 0\n  second_found = 0\n  temp = 0\n  print(4)\n  for i in range(row):\n   for j in range(col):\n    x = j%4\n    if temp%2 == 0:\n     if first_found == 0:\n      print(first[x], end=\' \')\n     else:\n      print(second[x], end=\' \')\n    else:\n     if(second_found == 0):\n      print(third[x], end=\' \')\n     else:\n      print(fourth[x], end=\' \')\n\n   if first_found == 0 and temp%2 == 0:\n    first_found = 1\n   elif first_found == 1 and temp%2 == 0:\n    first_found = 0\n   if second_found == 0 and temp%2 == 1:\n    second_found = 1\n   elif second_found == 1 and temp%2 == 1:\n    second_found = 0\n\n   temp += 1\n   print()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14127