P8749 [Lanqiao Cup 2021 NOI Qualifier B] Pascal's Triangle

The figure below is the well-known Pascal's Triangle:  If we list all numbers in order from top to bottom and from left to right, we get the following sequence: $1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, \ldots$ Given a positive integer $N$, output the position (which term) where $N$ first appears in the sequence.

Input one integer $N$.

Output one integer representing the answer.

For $20 \%$ of the test cases, $1 \leq N \leq 10$. For all test cases, $1 \leq N \leq 10^9$. Lanqiao Cup 2021, Round 1, Provincial Contest, Group B, Problem H. Translated by ChatGPT 5