1249_C2. Good Numbers (hard version)
The only difference between easy and hard versions is the maximum value of n.

You are given a positive integer number n. You really love good numbers so you want to find the smallest good number greater than or equal to n.

The positive integer is called good if it can be represented as a sum of distinct powers of 3 (i.e. no duplicates of powers of 3 are allowed).

For example:

  * 30 is a good number: 30 = 3^3 + 3^1, 
  * 1 is a good number: 1 = 3^0, 
  * 12 is a good number: 12 = 3^2 + 3^1, 
  * but 2 is not a good number: you can't represent it as a sum of distinct powers of 3 (2 = 3^0 + 3^0), 
  * 19 is not a good number: you can't represent it as a sum of distinct powers of 3 (for example, the representations 19 = 3^2 + 3^2 + 3^0 = 3^2 + 3^1 + 3^1 + 3^1 + 3^0 are invalid), 
  * 20 is also not a good number: you can't represent it as a sum of distinct powers of 3 (for example, the representation 20 = 3^2 + 3^2 + 3^0 + 3^0 is invalid). 



Note, that there exist other representations of 19 and 20 as sums of powers of 3 but none of them consists of distinct powers of 3.

For the given positive integer n find such smallest m (n ≤ m) that m is a good number.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 500) — the number of queries. Then q queries follow.

The only line of the query contains one integer n (1 ≤ n ≤ 10^{18}).

Output

For each query, print such smallest integer m (where n ≤ m) that m is a good number.

Example

Input


8
1
2
6
13
14
3620
10000
1000000000000000000


Output


1
3
9
13
27
6561
19683
1350851717672992089
```python
for _ in range(int(input())):
    n=int(input())
    a=[]
    b=[0]
    for i in range(50):
        a.append(3**i)
        b.append(b[-1]+a[-1])
        if b[-1]> n:
            break
    s=b[i+1]
    a=a[::-1]
    # print(s,a)

    for j in a:
        if s-j>=n:
            s-=j
    print(s)
```