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;

typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef pair<int,int> P;
typedef pair<ll,ll> PL;

#define INF 1<<30
#define LINF 1ll<<60ll
#define MOD 1000000007
#define pb(a) push_back(a)

#define _overload3(_1,_2,_3,_4,name,...) name
#define _rep(i,n) _repi(i,0,n)
#define _repi(i,a,b) for(int i=a, i##_len=(b); i<i##_len; ++i)
#define _repis(i,a,b,s) for(int i=a, i##_len(b); i<i##_len; i+=s)
#define REP(...) _overload3(__VA_ARGS__,_repis,_repi,_rep,)(__VA_ARGS__)

#define REPR(i, n) for(int i = n;i >= 0;--i)
#define REPARR(i, v) for(int i = 0;i < sz(v);++i)

#define all(vec) (vec.begin()),(vec.end())
#define sz(x) ((int)(x).size())
#define bit(n) (1ll<<(n))

template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}

#define YES(n) cout<<((n)?"YES":"NO")<<endl
#define Yes(n) cout<<((n)?"Yes":"No")<<endl
#define yes(n) cout<<((n)?"yes":"no")<<endl
#define poss(n) cout<<((n)?"possible":"impossible")<<endl
#define Poss(n) cout<<((n)?"Possible":"Impossible")<<endl
#define POSS(n) cout<<((n)?"POSSIBLE":"IMPOSSIBLE")<<endl

int main(){
    int x;
    cin>>x;
    int a=0;
    REP(i,x+1){
        a+=i;
        if(a>=x){
            cout<<i<<endl;
            break;
        }
    }
    return 0;
}