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 = 'import sys\nf=sys.stdin\n#f=open("test.txt","r")\nt=int(f.readline())\nfor r in range(t):\n n, m = map(int, f.readline().rstrip().split())\n if n == 1 and m == 1:\n  print("1")\n  print("1")\n elif n == 2 and m == 2:\n  print("2")\n  print("1 2")\n  print("1 2")\n elif n==2 and m==1:\n  print("1")\n  print("1")\n  print("1")\n elif n==1 and m==2:\n  print("1")\n  print("1 1")\n elif n==1 and m>2:\n  print("2")\n  #\n  for i in range(1,m+1):\n   if (i % 4 == 1 or i % 4 == 2):\n    print("1",end=" ")\n   else:\n    print("2",end=" ")\n elif n>2 and m==1:\n  print("\\n2")\n  for i in range(1, n + 1):\n   if (i % 4 == 1 or i % 4 == 2):\n    print("1")\n   else:\n    print("2")\n elif n==2 and m>2:\n  print("3")\n  #\n  for i in range(0,n):\n   for j in range(1,m+1):\n    if j%3==1:\n     print("1",end=" ")\n    elif j%3==2:\n     print("2", end=" ")\n    else:\n     print("3", end=" ")\n   print()\n elif n>2 and m==2:\n  print("3")\n  #\n  for i in range(1,n+1):\n   for j in range(1,m+1):\n    if i%3==1:\n     print("1",end=" ")\n    elif i%3==2:\n     print("2", end=" ")\n    else:\n     print("3", end=" ")\n   print()\n else:\n  print("4")\n  l = [[0 for x in range(m)] for x in range(n)]\n  for q in range(0,m):\n   if (q+1)%4!=0:\n    l[0][q] =(q+1)%4\n    l[1][q] =(q+1)%4\n   else:\n    l[0][q] =4\n    l[1][q] =4\n  for i in range(2,n):\n   for j in range(1,m-1):\n    l[i][j]=10-(l[i-1][j-1]+l[i-2][j]+l[i-1][j+1])\n   if(l[i][1]!=1):\n    l[i][0]=l[i][1]-1\n   else:\n    l[i][0] = 4\n   if(l[i][m-2]!=4):\n    l[i][m-1]=l[i][m-2]+1\n   else:\n    l[i][m-1]=1\n  for i in range(0,n):\n   for j in range(0,m):\n    print(l[i][j],end=" ")\n   print()\n\n\n\n\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15061