Two numbers and the four actions

Over two positive integers were executed the following four steps:

1. they were added;

2. the less number was subtracted from the larger;

3. they were multiplied;

4. the bigger number was divided by the smaller.

The results were added — and the number $n$ was obtained. Find all such pairs of numbers.

Input

One positive integer $n(1\le n\le 10^{12})$.

Output

Print on a separate lines the pairs of integers $(x,y),x\le y$, satisfying the problem. Couples must be ordered by increasing $x$. If there is no pair of numbers satisfying the condition, print "NO SOLUTION".

Examples