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 <bits/stdc++.h>
using namespace std;

const double pi  = 2 * acos(0.0);
const double eps = 1e-8;

#define REP(i,a,b) for(int i=(a); i<(b);++i)
#define rep(i,n) REP(i,0,n)
#define INF (1<<29)
#define INFLL (1LL<<61)

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

typedef int Cost;
struct Edge {
  int src, dst; Cost cost;
  Edge(int s, int d, Cost c) : src(s), dst(d), cost(c) {}
};
typedef vector<Edge>  Edges;
typedef vector<Edges> Graph;
typedef vector<Cost>  Array;
typedef vector<Array> Matrix;

int dx[8] = {0, 1, 0, -1, 1, -1, 1, -1};
int dy[8] = {1, 0, -1, 0, 1, -1, -1, 1};

int main(void) {
  ios_base::sync_with_stdio(false); cin.tie(0);
  int X; cin >> X;
  for (int i = 0; i <= 100000; i++) {
    if (i*(i+1)/2 < X)
      continue;
    cout << i << endl;
    break;
  }
  return 0;
}