An interesting Sequence ~ Multiplex Coder

You are given an integer

$K$ .

Consider an integer sequence $A = [A_{1}, A_{2}, \dots, A_{N}]$ .

Define another sequence $S$ of length $N$ , such that $S_{i} = A_{1} + A_{2} + \dots + A_{i}$ for each $1 \leq i \leq N$ .

$A$ is said to be interesting if $A_{i} + S_{i} = K$ for every $1 \leq i \leq N$ .

Find the maximum length of an interesting sequence. If there are no interesting sequences, print $0$ .

Input Format

The first line of input contains an integer $T$ , denoting the number of test cases. The description of $T$ test cases follows.
Each test case consists of a single line of input, which contains a single integer $K$ .

Output Format

For each test case, print a new line containing one integer — the maximum length of an interesting sequence for a given value of $K$ .

Constraints

$1 \leq T \leq 5000$
$1 \leq K \leq 10^{9}$

Sample Input 1

2
8
4

Sample Output 1

3
2

Explanation

Test Case $1$ : Consider the sequence $A = [4, 2, 1]$ . $S = [4, 4 + 2, 4 + 2 + 1] = [4, 6, 7]$ . The sum of the corresponding elements of $A$ and $S$ are $4 + 4 = 8$ , $2 + 6 = 8$ and $1 + 7 = 8$ . Thus $A$ is an interesting sequence of size $3$ .

Test Case $2$ : Consider the sequence $A = [2, 1]$ . $S = [2, 2 + 1] = [2, 3]$ . The sum of the corresponding elements of $A$ and $S$ are $2 + 2 = 4$ and $1 + 3 = 4$ . Thus $A$ is an interesting sequence of size $2$ .

It's guaranteed that, in both examples above, there doesn't exist a longer sequence satisfying the problem constraints.