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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.

Examples

Input

6

Output

3

Input

2

Output

2

Input

11

Output

5

inputFormat

Input

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

X

outputFormat

Output

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

Examples

Input

6

Output

3

Input

2

Output

2

Input

11

Output

5

样例

6

3