There are N friends who decided to play the game of musical chairs one day.

Initially they decide a number K and with each passing round they remove exactly K chairs. Hence, in each round exactly K players are eliminated. The game stops when less than or exactly K players remain in the game.

Now, Chef wants to figure out for how many possible values of K there will be exactly one winner in the game.

------ Input Format ------

• The first line contains T - the number of test cases. Then the test cases follow.
• The first line of each test case contain N - the number of friends in the game.

------ Output Format ------

For each test case, output in a single line a integer that denotes the number of values of K for which there will be exactly one winner.

------ Constraints ------

$1 ≤ T ≤ 100$
$2 ≤ N ≤ 10^{9}$

----- Sample Input 1 ------
3
2
3
4

----- Sample Output 1 ------
1
2
2

----- explanation 1 ------
- Test case $1$: There will be only one winner if the friends remove exactly $1$ chair each round.
- Test case $2$: There will be only one winner if the friends remove $1$ or $2$ chairs each round.
- Test case $3$: There will be only one winner if the friends remove $1$ or $3$ chairs each round. If they remove $2$ chairs then there will be two winners.

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