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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"math"
)

var X int

func main() {
	fmt.Scan(&X)

	/* 1+2+3+...+t >= X となる最小のtを考える */
	var i int
	for i*(i+1)/2 < X {
		i++
	}
	fmt.Println(i)
}

/*  ----------------------------------------  */

func gcd(x, y uint64) uint64 {
	if x%y == 0 {
		return y
	} else {
		r := x % y
		return gcd(y, r)
	}
}

func combination(x, y int) int {
	return permutation(x, y) / permutation(y, y)
}

func permutation(x, y int) int {
	var ans int = 1
	for i := x - y; 0 < i; i-- {
		ans *= i
	}
	return ans
}

func max(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Max(float64(x[i]), float64(res)))
	}
	return res
}

func min(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Min(float64(x[i]), float64(res)))
	}
	return res
}

func pow(x, y int) uint64 { return uint64(math.Pow(float64(x), float64(y))) }
func abs(x int) int       { return int(math.Abs(float64(x))) }
func floor(x int) int     { return int(math.Floor(float64(x))) }
func ceil(x int) int      { return int(math.Ceil(float64(x))) }

type si struct {
	s int
	i int
}

type SortBy []si

func (a SortBy) Len() int           { return len(a) }
func (a SortBy) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
func (a SortBy) Less(i, j int) bool { return a[i].s < a[j].s }