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: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <stdint.h> // uint64_t
#include <math.h>

#define max(a,b) ((a) > (b) ? (a) : (b))
#define min(a,b) ((a) > (b) ? (b) : (a))
#define BUF_SIZE 20

// size: specify sizeof(str)
int get_str(char *str, int size) {
    if(!fgets(str, size, stdin)) return -1;
    return 0;
}

uint64_t get_int(void) {
  uint64_t num;
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return 0;
  sscanf(line, "%llu", &num);
#else
#error
#endif
  return num;
}

int main(void) {
    uint64_t num = get_int();
    uint64_t num_2 = sqrt(0.5 + num);
    uint64_t i;
    for(i = num_2; i >= 1; i--) {
        if(num%i) continue;
        printf("%llu\n", i + (num/i) - 2);
        return 0;
    }
    return 0;
}