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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <iostream>
#include <memory.h>
#include <math.h>
#include <assert.h>
#include <queue>
#include <map>
#include <set>
#include <string>
#include <algorithm>
#include <functional>
#include <vector>
#include <stack>
#include <bitset>
#include <sstream> 
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> Pi;
typedef pair<ll,ll> Pll;

#define Fi first
#define Se second
#define pb(x) push_back(x)
#define sz(x) (int)x.size()
#define rep(i, n) for(int i=0;i<n;i++)
#define repp(i, n) for(int i=1;i<=n;i++)
#define all(x) x.begin(), x.end()

#define ABS(x) (((x) > 0 ) ? (x) : (-(x)))
#define MAX2(x, y) (((x) > (y)) ? (x) : (y))
#define MIN2(x, y) (((x) < (y)) ? (x) : (y))
#define MAX3(x, y, z) ( (x) > (y)  ? ( (x) > (z) ? (x) : (z)  ) : ( (y) > (z) ? (y) : (z) )  )
#define MIN3(x, y, z) ( (x) < (y)  ? ( (x) < (z) ? (x) : (z)  ) : ( (y) < (z) ? (y) : (z) )  )
#define MID3(val1,val2,val3) MAX2(MIN2(MAX2(val1,val2),val3),MIN2(val1,val2))


#define geti1(X) scanf("%d",&X)
#define geti2(X,Y) scanf("%d%d",&X,&Y)
#define geti3(X,Y,Z) scanf("%d%d%d",&X,&Y,&Z)
#define geti4(X,Y,Z,W) scanf("%d%d%d%d",&X,&Y,&Z,&W)

#define GET_MACRO(_1,_2,_3,_4,NAME,...) NAME
#define geti(...) GET_MACRO(__VA_ARGS__, geti4, geti3, geti2, geti1) (__VA_ARGS__)

#define INF 987654321
#define IINF 987654321987654321

int N,M,K,T,tc;
int main(void){
	ll x; cin >> x;
	ll ans = 1;
	while(true){
		ll t = (ans)*(ans+1)/2;
		if( t >= x ) break;
		ans++;
	}
	cout << ans;

}