Chef is a very experienced and well-known cook. He has participated in many cooking competitions in the past — so many that he does not even remember them all.
One of these competitions lasted for a certain number of days. The first day of the competition was day $S$ of the week (i.e. Monday, Tuesday etc.) and the last day was day $E$ of the week. Chef remembers that the duration of the competition (the number of days between the first and last day, inclusive) was between $L$ days and $R$ days inclusive. Is it possible to uniquely determine the exact duration of the competition? If so, what is this duration?

-----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 strings $S$ and $E$, followed by a space and two space-separated integers $L$ and $R$.

-----Output-----
For each test case, print a single line containing:
- the string "impossible" if there is no duration consistent with all given information
- the string "many" if there is more than one possible duration
- one integer — the duration of the competition, if its duration is unique

-----Constraints-----
- $1 \le T \le 10,000$
- $1 \le L \le R \le 100$
- $S$ is one of the strings "saturday", "sunday", "monday", "tuesday", "wednesday", "thursday" or "friday"
- $E$ is one of the strings "saturday", "sunday", "monday", "tuesday", "wednesday", "thursday" or "friday"

-----Subtasks-----
Subtask #1 (100 points): original constraints

-----Example Input-----
3
saturday sunday 2 4
monday wednesday 1 20
saturday sunday 3 5

-----Example Output-----
2
many
impossible

```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 = '# cook your dish here\nd=["saturday","sunday","monday","tuesday","wednesday","thursday","friday"]\nt=int(input())\nfor i in range(t):\n s,e,l,r=map(str,input().split())\n l,r=int(l),int(r)\n v=(d.index(e)-d.index(s)+8)%7\n c=r+1\n for i in range(l,r+1):\n  if i%7==v:\n   c=i\n   break\n if c>r:\n  print(\'impossible\')\n elif c+7<=r:\n  print(\'many\')\n else:\n  print(c)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13319