No submission language available for this problem.

Description

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). Description of the test cases follows.

A test case consists of only one line, containing one integer $n$ ($1\le n\le 10^{12}$).

Output

For each test case print the answer on a separate line.

If $n$ can not be represented as the sum of distinct powerful numbers, print $-1$.

Otherwise, print a single positive integer  — the minimum possible value of $k$.

Samples

4
7
11
240
17179869184

2
3
4
1

Note

In the first test case, $7$ can be represented as $7=1+6$, where $1$ and $6$ are powerful numbers. Because $7$ is not a powerful number, we know that the minimum possible value of $k$ in this case is $k=2$.

In the second test case, a possible way to represent $11$ as the sum of three powerful numbers is $11=1+4+6$. We can show that there is no way to represent $11$ as the sum of two or less powerful numbers.

In the third test case, $240$ can be represented as $240=24+32+64+120$. Observe that $240=120+120$ is not a valid representation, because the powerful numbers have to be distinct.

In the fourth test case, $17179869184=2^{34}$, so $17179869184$ is a powerful number and the minimum $k$ in this case is $k=1$.