CF1725G Garage

Pak Chanek plans to build a garage. He wants the garage to consist of a square and a right triangle that are arranged like the following illustration. Define $ a $ and $ b $ as the lengths of two of the sides in the right triangle as shown in the illustration. An integer $ x $ is suitable if and only if we can construct a garage with assigning positive integer values for the lengths $ a $ and $ b $ ( $ a

The only line contains a single integer $ N $ ( $ 1 \leq N \leq 10^9 $ ).

An integer that represents the $ N $ -th smallest suitable number.

The $ 3 $ -rd smallest suitable number is $ 7 $ . A square area of $ 7 $ can be obtained by assigning $ a=3 $ and $ b=4 $ .