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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
 
#define sl(x) scanf("%ld", &x)
#define ss(x) scanf("%s", x)
#define pl(x) printf("%ld\n", x)
#define pd(x) printf("%lf\n", x)
#define ps(x) printf("%s\n", x)
 
#define INF 1000000000000000000
#define MOD 1000000007
 
#define MIN(a,b) (((a)<(b))?(a):(b))
#define MAX(a,b) (((a)>(b))?(a):(b))

int compare_long(const void *a, const void *b) {
	return *(long*)a - *(long*)b;
}
 
int main() {
	long X;
	long sum = 0;
	long i, j;
	
	sl(X);
	
	for(i=1;i<=X;i++) {
		sum += i;
		if(sum >= X) {
			break;
		}
	}
	
	pl(i);
	
	return 0;
}