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 = 't=int(input())\nfor w in range(t):\n inp = list(map(int,input().split()))\n row=inp[0]\n col=inp[1]\n flag=0\n if(min(row,col)==1):\n  if(max(row,col)>=3):\n   print(2)\n  else:\n   print(1)\n  if(1):\n   a=[0 for i in range(max(col,row))]\n   count=0\n   it=1\n   for i in range(max(col,row)):\n    if(count==2):\n     if(it==1):\n      it=2\n     else:\n      it=1\n     a[i]=it\n     count=1\n     continue\n    else:\n     a[i]=it\n     count+=1\n   if(row==1):\n    for item in a:\n     print(item,end=" ")\n    print(" ")\n   \n   else:\n    for item in a:\n     print(item)\n elif(min(row,col)==2):\n  if(max(row,col)==2):\n   print(2)\n   print(2,end=" ")\n   print(2)\n   print(1,end=" ")\n   print(1)\n  else:\n   a=[[0 for i in range(max(row,col))]for j in range(2)]\n   print(3)\n   it=3\n   count=1\n   for i in range(max(row,col)):\n    if(count==1):\n     a[0][i]=it\n     count+=1\n     continue\n    else:\n     if(count==2):\n      it-=1\n      if(it==0):\n       it=3\n      a[0][i]=it\n      count=1\n      continue\n   it=2\n   count=2\n   for i in range(max(row,col)):\n    if(count==1):\n     a[1][i]=it\n     count+=1\n     continue\n    else:\n     if(count==2):\n      it-=1\n      if(it==0):\n       it=3\n      a[1][i]=it\n      count=1\n      continue\n   if(row==2):\n    for i in range(max(row,col)):\n     print(a[0][i],end=" ")\n    print(" ")\n    for i in range(max(row,col)):\n     print(a[1][i],end=" ")\n    print(\' \')\n   else:\n    for i in range(max(row,col)):\n     print(a[0][i],end=" ")\n     print(a[1][i])\n\n else:\n  print(4)\n  a=[[0 for i in range(col)]for j in range(row)]\n  a[0][0]=2\n  a[1][0]=2\n  a[0][1]=3\n  a[1][1]=3\n  for i in range(2,col,2):\n   if(a[0][i-2]==2):\n    a[0][i]=1\n    a[1][i]=1\n   else:\n    a[0][i]=2\n    a[1][i]=2\n  for i in range(3,col,2):\n   if(a[0][i-2]==3):\n    a[0][i]=4\n    a[1][i]=4\n   else:\n    a[0][i]=3\n    a[1][i]=3\n  for i in range(col):\n   for j in range(2,row):\n    if(a[j-2][i]==2):\n     a[j][i]=1\n    elif(a[j-2][i]==1):\n     a[j][i]=2\n    elif(a[j-2][i]==3):\n     a[j][i]=4\n    elif(a[j-2][i]==4):\n     a[j][i]=3\n  for i in range(row):\n   for j in range(col):\n    print(a[i][j],end=\' \')\n   print(" ")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15267