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. You must find all such pairs of numbers.

Input

One positive integer n (1 ≤ n ≤ 1012).

Output

Print on a separate lines the pairs of integers x ≤ y, satisfying the problem. Couples must be ordered by increasing x. If there is no pair of numbers satisfying the condition, display "**NO SOLUTION**" (without the quotes).