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 fill_grid_max():\n A = [[0 for j in range(50)] for i in range(50)]\n B = [[1,1,2,2],[3,3,4,4],[2,2,1,1],[4,4,3,3]]\n for i in range(50):\n  for j in range(50):\n   A[i][j] = B[i%4][j%4]\n return A\n \ndef calculate_k(A):\n k = 0\n for row in A:\n  k = max(k,max(row))\n return k\n \ndef print_output(A,k,n,m):\n print(k)\n for i in range(n):\n  for j in range(m):\n   print(A[i][j], end = ' ')\n  print()\n\nt = int(input())\nA = fill_grid_max()\nfor test in range(t):\n n,m = map(int,input().split())\n if n==1 and m==1:\n  print(1)\n  print(1)\n elif n==1:\n  B = A[0][:m]\n  k = max(B)\n  print(k)\n  for x in B:\n   print(x,end = ' ')\n  print()\n elif m==1:\n  B = [[] for x in range(n)]\n  for i in range(n):\n   B[i].append(A[0][i])\n  k = max(A[0][:n])\n  print_output(B,k,n,m)\n elif n==2 and m==2:\n  k = 2\n  B = [[1,1],[2,2]]\n  print_output(B,k,n,m)\n elif n==2:\n  k = 3\n  B = [[0 for x in range(m)] for y in range(n)]\n  C = [[1,2,3],[1,2,3]]\n  for i in range(n):\n   for j in range(m):\n    B[i][j] = C[i][j%3]\n  print_output(B,k,n,m)\n elif m==2:\n  k = 3\n  B = [[0 for x in range(m)] for y in range(n)]\n  C = [[1,1],[2,2],[3,3]]\n  for i in range(n):\n   for j in range(m):\n    B[i][j] = C[i%3][j]\n  print_output(B,k,n,m)\n if n>=3 and m>=3:\n  print_output(A,4,n,m)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 32295