You will be given an array of strings. The words in the array should mesh together where one or more letters at the end of one word will have the same letters (in the same order) as the next word in the array. But, there are times when all the words won't mesh. 

Examples of meshed words:

  "apply" and "plywood"
  
  "apple" and "each"
  
  "behemoth" and "mother"
  
Examples of words that don't mesh:

  "apply" and "playground"
  
  "apple" and "peggy"
  
  "behemoth" and "mathematics"
  

If all the words in the given array mesh together, then your code should return the meshed letters in a string.
You won't know how many letters the meshed words have in common, but it will be at least one.

If all the words don't mesh together, then your code should return `"failed to mesh"`.

Input: An array of strings. There will always be at least two words in the input array.

Output: Either a string of letters that mesh the words together or the string `"failed to mesh"`.


## Examples

#1:

```
["allow", "lowering", "ringmaster", "terror"] --> "lowringter"
```
because:

* the letters `"low"` in the first two words mesh together
* the letters `"ring"` in the second and third word mesh together
* the letters `"ter"` in the third and fourth words mesh together.


#2:

```
["kingdom", "dominator", "notorious", "usual", "allegory"] --> "failed to mesh"
```

Although the words `"dominator"` and `"notorious"` share letters in the same order, the last letters of the first word don't mesh with the first letters of the second word.

```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 = 'def word_mesh(arr):\n    overlaps = [\n        max(\n            filter(prev.endswith, (word[:k] for k in range(len(word)+1)))\n        ) for prev,word in zip(arr, arr[1:])\n    ]\n    return "".join(overlaps) if all(overlaps) else "failed to mesh"'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'word_mesh'
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: 6939