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 <math.h>
#include <stdlib.h>

int main(void){
    int N;
    int flag = 0;
    scanf("%d", &N);
    int min = N;
    int n = (int)sqrt(N);
    int A[N][N];
    for (int i = 1; i <= N; i++){
        for (int j = i; j <= N; j++){
            A[i - 1][j - 1] = i * j;
        }
    }
    int a = 0;
    int b = 0;
    for (int k = n; abs(k) < N; k = n + a){
    //for (int k = 1; k <= N; k++){
        for (int i = k; i <= N; i++){
            if (A[k - 1][i - 1] == N){
                if (min > k + i - 2){
                    min = k + i - 2;
                }
                flag = 1;
            }
            if(flag){
                break;
            }
        }
        //flag = 0;
        if(flag){
            break;
        }
        b += 1;
        a = pow(-1, b) * b;
    }
    printf("%d\n", min);
    
    return 0;
}