Find the number of Ludic numbers less than or equal to $N$.

Input

The first line contains $T$ ($1 \le T \le 1000$), the number of test cases.

Each test case contains a single integer $N$ ($1 \le N \le 10^9$).

Output

For each test case, output the number of Ludic numbers less than or equal to $N$.

Example

Input

10
1
2
3
4
5
10
100
1000
1000000
1000000000

Output

1
2
3
3
4
5
24
142
66164
43956562

Note

• See LUDIC2 for a harder version.
• Other references for the Ludic numbers: Ludic numbers or A003309.