A. Greatest Convex

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an integer k�. Find the largest integer x�, where 1≤x<k1≤�<�, such that x!+(x−1)!†�!+(�−1)!† is a multiple of ‡‡ k�, or determine that no such x� exists.

†† y!�! denotes the factorial of y�, which is defined recursively as y!=y⋅(y−1)!�!=�⋅(�−1)! for y≥1�≥1 with the base case of 0!=10!=1. For example, 5!=5⋅4⋅3⋅2⋅1⋅0!=1205!=5⋅4⋅3⋅2⋅1⋅0!=120.

‡‡ If a� and b� are integers, then a� is a multiple of b� if there exists an integer c� such that a=b⋅c�=�⋅�. For example, 1010 is a multiple of 55 but 99 is not a multiple of 66.

Input

The first line contains a single integer t� (1≤t≤1041≤�≤104) — the number of test cases. The description of test cases follows.

The only line of each test case contains a single integer k� (2≤k≤1092≤�≤109).

Output

For each test case output a single integer — the largest possible integer x� that satisfies the conditions above.

If no such x� exists, output −1−1.

Example

input

Copy

output

Copy

Note

In the first test case, 2!+1!=2+1=32!+1!=2+1=3, which is a multiple of 33.

In the third test case, 7!+6!=5040+720=57607!+6!=5040+720=5760, which is a multiple of 88.

解题说明：此题是一道数学题，知道(n-1)!+(n-2)!=n! 这个公式就知道此题答案了。

#include <stdio.h>int main() {int t;scanf("%d", &t);while (t--) {int n;scanf("%d", &n);printf("%d\n", n - 1);}return 0;
}

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