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 Python (3.4.3) (judge verdict: Wrong Answer)

import math
x = int(input())
n = math.ceil(math.sqrt(x*2))
s = [list(map(int,bin(x)[2:].zfill(n))) for x in range(2**n)]
t = 0
c = 0
min = x
for i in range(2**n):
    for j in range(len(s[i])):
        t+=s[i][j]*(j+1)
        if s[i][j]==1:
            c =j+1
    if t==x and c<min:
        min =c
print(c)