You are given an integer $n$.

Your task is to find two positive (greater than $0$) integers $a$ and $b$ such that $a+b=n$ and the least common multiple (LCM) of $a$ and $b$ is the minimum among all possible values of $a$ and $b$. If there are multiple answers, you can print any of them.

Input

The first line contains a single integer $t$ ($1 \le t \le 100$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($2 \le n \le 10^9$).

Output

For each test case, print two positive integers $a$ and $b$ — the answer to the problem. If there are multiple answers, you can print any of them.

Note

In the second example, there are $8$ possible pairs of $a$ and $b$:

• $a = 1$, $b = 8$, $LCM(1, 8) = 8$;
• $a = 2$, $b = 7$, $LCM(2, 7) = 14$;
• $a = 3$, $b = 6$, $LCM(3, 6) = 6$;
• $a = 4$, $b = 5$, $LCM(4, 5) = 20$;
• $a = 5$, $b = 4$, $LCM(5, 4) = 20$;
• $a = 6$, $b = 3$, $LCM(6, 3) = 6$;
• $a = 7$, $b = 2$, $LCM(7, 2) = 14$;
• $a = 8$, $b = 1$, $LCM(8, 1) = 8$.

In the third example, there are $5$ possible pairs of $a$ and $b$:

• $a = 1$, $b = 4$, $LCM(1, 4) = 4$;
• $a = 2$, $b = 3$, $LCM(2, 3) = 6$;
• $a = 3$, $b = 2$, $LCM(3, 2) = 6$;
• $a = 4$, $b = 1$, $LCM(4, 1) = 4$.

Samples

4
2
9
5
10

1 1
3 6
1 4
5 5