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>
# define ll int64_t
# define rep(i,n) for(ll i=0;i<n;i++)
# define rrep(i,n) for(ll i=1;i<=n;i++)
# define ALL(x) (x).begin(), (x).end()
# define SZ(x) ((int)(x).size())
# define pb push_back
# define mod 1000000007

using namespace std;

bool compare_by_b(pair<string,ll> a,pair<string,ll> b){
    if(a.second != b.second) return a.second<b.second;
    else return a.first<b.first;
}

bool my_compare(pair<string,ll> a,pair<string,ll> b){
    
    if(a.first != b.first) return a.first<b.first;
    if(a.second != b.second) return a.second>b.second;
    else return true;
}

ll factorial(ll n){
    ll x=1;
    rrep(i,n) x*=i;
    return x;
}

ll gcd(ll a,ll b)
{
   if (a%b == 0) return(b);
   else return(gcd(b,a%b));
}

ll lcm(ll a,ll b)
{
   return a/gcd(a,b)*b;
}



int main(){
    ll x,n=1;
    cin>>x;
    while(n*(n+1)/2<x) n++;
    cout<<n<<endl;
    return 0;
}