p03781 AtCoder Regular Contest 070 - Go Home
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
```python
import math
X = int(input())
low_N = (-1 + (1 + 8 * X)**0.5) / 2
high_N = (1 + (1 + 8 * X)**0.5) / 2
if low_N % 1 == 0:
    print(int(low_N))
else:
    print(math.floor(high_N))
```