Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two and 3 squares with side three. The total number of distinct squares in a 3 × 5 table is 15 + 8 + 3 = 26.
输入描述:
The first line of the input contains a single integer x (1 ≤ x ≤ 1018) — the number of squares inside the tables Spongebob is interested in.
输出描述:
First print a single integer k — the number of tables with exactly x distinct squares inside.Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality — in the order of increasing m.
示例1
输出
6<br />1 26<br />2 9<br />3 5<br />5 3<br />9 2<br />26 1<br />2<br />1 2<br />2 1<br />4<br />1 8<br />2 3<br />3 2<br />8 1<br />
备注:
In a 1 × 2 table there are 21 × 1 squares. So, 2 distinct squares in total.In a 2 × 3 table there are 61 × 1 squares and 22 × 2 squares. That is equal to 8 squares in total.
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