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: Time Limit Exceeded)

#include<stdio.h>
long long num,min,mini;
long long work(long long n,long long hm,long long time)
{
    //printf("work %lld != %lld %lld %lld\n",num,n,hm,time);
    if(n==num) return time-1;
    if(n+time>num) return 0;
    long long c= work(n+time,hm+1,time+1);
    long long d= work(n,hm,time+1);
    if(d<=0)
    {
        //printf("return c= %lld\n",c);
        return c;
    }
    else if(c<=0)
    {
        //printf("return d= %lld\n",d);
        return d;
    }
    else if(c>d) return d;
    return c;
}
main()
{
    scanf("%lld",&num);
    printf("%lld\n",work(0,0,1));
}