Two numbers and the four actions#1613
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Two numbers and the four actions

1 second
128 megabytes
Easy

Two positive integers undergo the following four operations:

  1. They are added.

  2. The smaller number is subtracted from the larger.

  3. They are multiplied.

  4. The larger number is divided by the smaller.

The results of these operations are summed to obtain the number . Find all pairs of such numbers.

Input

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

Output

Print each pair of integers , x \leq y, that satisfy the condition, on a separate line. The pairs must be sorted in increasing order of . If there are no pairs satisfying the condition, print "NO SOLUTION".

Examples

Example 1

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Example 2

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Example 3

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