Problem:

A tree is called $K-Good (K \geq 1)$ if all the nodes of the tree have exactly $K$ children except the leaves. For given count of leaves $M (M \geq 2)$, find the number of possible values of $K$.

 Input Format:

• The first line of the input contains a single integer $T$ - 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 $M$.

Output Format:

• For each test case, print the number of possible values of $K$ for given count of leaves $M$.

Constraints:

• $1 \leq T \leq 10^3$
• $2 \leq M \leq 10^{9}$