There is a strange printer with the following two special requirements:

On each turn, the printer will print a solid rectangular pattern of a single color on the grid. This will cover up the existing colors in the rectangle.
Once the printer has used a color for the above operation, the same color cannot be used again.

You are given a m x n matrix targetGrid, where targetGrid[row][col] is the color in the position (row, col) of the grid.
Return true if it is possible to print the matrix targetGrid, otherwise, return false.
 
Example 1:

Input: targetGrid = [[1,1,1,1],[1,2,2,1],[1,2,2,1],[1,1,1,1]]
Output: true

Example 2:

Input: targetGrid = [[1,1,1,1],[1,1,3,3],[1,1,3,4],[5,5,1,4]]
Output: true

Example 3:
Input: targetGrid = [[1,2,1],[2,1,2],[1,2,1]]
Output: false
Explanation: It is impossible to form targetGrid because it is not allowed to print the same color in different turns.
Example 4:
Input: targetGrid = [[1,1,1],[3,1,3]]
Output: false

 
Constraints:

m == targetGrid.length
n == targetGrid[i].length
1 <= m, n <= 60
1 <= targetGrid[row][col] <= 60

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'from collections import deque\n\nclass Solution:\n    def isPrintable(self, targetGrid: List[List[int]]) -> bool:\n        grids = targetGrid\n        num_to_range = dict()\n        for i, row in enumerate(targetGrid):\n            for j, val in enumerate(row):\n                if val not in num_to_range:\n                    # up, down, left, right\n                    num_to_range[val] = [i, i, j, j]\n                num_to_range[val][0] = min(num_to_range[val][0], i)\n                num_to_range[val][1] = max(num_to_range[val][1], i)\n                num_to_range[val][2] = min(num_to_range[val][2], j)\n                num_to_range[val][3] = max(num_to_range[val][3], j)\n        #print(num_to_range)\n        \n        m = len(grids)\n        n = len(grids[0])\n        grid_list = [[list() for j in range(n)] for i in range(m)]\n        for num, val in list(num_to_range.items()):\n            for i in range(val[0], val[1]+1):\n                for j in range(val[2], val[3]+1):\n                    grid_list[i][j].append(num)\n\n        paths = {val: set() for val in list(num_to_range)}\n        for i, row in enumerate(targetGrid):\n            for j, val in enumerate(row):\n                for parent in grid_list[i][j]:\n                    if parent != val:\n                        paths[parent].add(val)\n                    \n        parent_counter = {val: 0 for val in list(num_to_range)}\n        for parent, childs in list(paths.items()):\n            for child in childs:\n                parent_counter[child] += 1\n        \n        queue = deque()\n        for child, cnt in list(parent_counter.items()):\n            if cnt == 0:\n                queue.append(child)\n        \n        seen = set()\n        while queue:\n            parent = queue.popleft()\n            seen.add(parent)\n            for child in paths[parent]:\n                parent_counter[child] -= 1\n                if parent_counter[child] == 0:\n                    queue.append(child)\n                \n        \n        \n        return len(seen) == len(num_to_range)\n                \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isPrintable'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 12026