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 $$$b$$$:

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

Minimum LCM

Examples