Problem:
Score : 300 points

Problem Statement

Takahashi is standing on a multiplication table with infinitely many rows and columns.

The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).

In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).

Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the minimum number of moves needed to reach a square that contains the integer N.

Sample Input 1

10

Sample Output 1

5

(2,5) can be reached in five moves. We cannot reach a square that contains 10 in less than five moves.

Sample Input 2

50

Sample Output 2

13

(5, 10) can be reached in 13 moves.

Sample Input 3

10000000019

Sample Output 3

10000000018

Both input and output may be enormous.

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)


#include <stdio.h>
#include <stdlib.h>

#define x 10000

int compare_int(const void*a, const void *b){
	return *(long long int*)a - *(long long int*)b;
}

int main(void) {

	unsigned long long int a[x][x]={{0}};
	unsigned long long int b[x]={0};
	unsigned long long int n,i,j,left,right, m=0,cent;

	scanf("%lld", &n);

	for(i=1;i<n+1;i++){
		for(j=1;j<n+1;j++){
			a[i][j]=i*j;
		}
	}

	for(i=1;i<n+1;i++){
		left =1;
		right = n;

		while(1){
			cent =(left+right)/2;

			if(n==a[i][cent]){
				b[m]=i+cent-2;
				m++;
				break;
			}

			if(n > a[i][cent]){
				left = cent+1;
			}else{
				right =cent-1;
			}
			if(left>=right){
				break;
			}
		}
	}

	qsort(b,m,sizeof(long long int),compare_int);
	printf("%lld",b[0]);
	return EXIT_SUCCESS;
}