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 = 'from sys import stdin,stdout\r\n\r\n\r\ndef power(x, y, p): \r\n\r\n    res = 1; # Initialize result \r\n\r\n  \r\n\r\n    # Update x if it is  \r\n\r\n    # more than or equal to p \r\n\r\n    x = x % p;  \r\n\r\n  \r\n\r\n    while (y > 0):  \r\n\r\n          \r\n\r\n        # If y is odd, multiply \r\n\r\n        # x with the result \r\n\r\n        if (y & 1): \r\n\r\n            res = (res * x) % p; \r\n\r\n  \r\n\r\n        # y must be even now \r\n\r\n        y = y >> 1; # y = y/2 \r\n\r\n        x = (x * x) % p; \r\n\r\n          \r\n\r\n    return res; \r\n\r\n \r\ndef sin():\r\n    return stdin.readline()\r\n\r\ndef out(s):\r\n    stdout.write(str(s)+"\\n")\r\n    \t\r\nm=1000000007\r\nfor i in range(int(input())):\r\n    n=sin()[:-1]\r\n    remainderB = 0; \r\n    for i in range(len(n)):\r\n        remainderB = ((remainderB * 10 + \r\n\r\n                   ord(n[i]) - 48) % \r\n\r\n                   (m - 1)); \r\n    out((power(2, remainderB, m)*5)%m); '
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13501