On her way to ChefLand, Marichka noticed $10^K$ road signs (numbered $0$ through $10^K - 1$). For each valid $i$, the sign with number $i$ had the integer $i$ written on one side and $10^K-i-1$ written on the other side.
Now, Marichka is wondering — how many road signs have exactly two distinct decimal digits written on them (on both sides in total)? Since this number may be large, compute it modulo $10^9+7$.
For example, if $K = 3$, the two integers written on the road sign $363$ are $363$ and $636$, and they contain two distinct digits $3$ and $6$, but on the road sign $362$, there are integers $362$ and $637$, which contain four distinct digits — $2$, $3$, $6$ and $7$. On the road sign $11$, there are integers $11$ and $988$, which contain three distinct digits — $1$, $9$ and $8$.

-----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 a single integer $K$.

-----Output-----
For each test case, print a single line containing one integer — the number of road signs with exactly two digits, modulo $10^9+7$.

-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le K \le 10^9$

-----Subtasks-----
Subtask #1 (20 points): $1 \le T, K \le 5$
Subtask #2 (80 points): original constraints

-----Example Input-----
1
1

-----Example Output-----
10

```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\nimport math\nt=int(input())\nwhile(t>0):\n    k=int(input())\n    j=0\n    h=math.pow(10,k)-1\n    h=int(h)\n    c=0\n    for i in range(h+1):\n        ab=[]\n        if(i==0):\n            if(i not in ab):\n                ab.append(i)\n            p=h-i\n            while(p>0):\n                g=p%10\n                if(g not in ab):\n                    ab.append(g)\n                p=p//10\n        elif(i==h):\n            if(i not in ab):\n                ab.append(h-i)\n            p=i\n            while(p>0):\n                g=p%10\n                if(g not in ab):\n                    ab.append(g)\n                p=p//10\n                \n        else:\n            p=i\n            while(p>0):\n                g=p%10\n                if (g not in ab):\n                    ab.append(g)\n                p=p//10\n            p=h-i\n            while(p>0):\n                g=p%10\n                if(g not in ab):\n                    ab.append(g)\n                p=p//10\n        if(len(ab)==2):\n            c+=1\n    print(c)\n    t-=1\n\t    '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13553