Problem:
Score : 200 points

Problem Statement

There is a kangaroo at coordinate 0 on an infinite number line that runs from left to right, at time 0.
During the period between time i-1 and time i, the kangaroo can either stay at his position, or perform a jump of length exactly i to the left or to the right.
That is, if his coordinate at time i-1 is x, he can be at coordinate x-i, x or x+i at time i.
The kangaroo's nest is at coordinate X, and he wants to travel to coordinate X as fast as possible.
Find the earliest possible time to reach coordinate X.

Constraints

X is an integer.

1≤X≤10^9

Input

The input is given from Standard Input in the following format:

X

Output

Print the earliest possible time for the kangaroo to reach coordinate X.

Sample Input 1

6

Sample Output 1

3

The kangaroo can reach his nest at time 3 by jumping to the right three times, which is the earliest possible time.

Sample Input 2

2

Sample Output 2

2

He can reach his nest at time 2 by staying at his position during the first second, and jumping to the right at the next second.

Sample Input 3

11

Sample Output 3

5

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

def main():
    N = int(input())
    from itertools import accumulate
    S = [i for i in accumulate(range(1, N+1))]

    def is_ok(mid):
        if N <= S[mid]:
            return True
        else:
            return False

    def binary_search_meguru():
        left = -1
        right = N
        while right - left > 1:
            mid = left + ((right - left) // 2)
            if is_ok(mid):
                right = mid
            else:
                left = mid
        return right

    ans = binary_search_meguru() + 1
    print(ans)


if __name__ == '__main__':
    main()