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 JavaScript (node.js v5.12) (judge verdict: Accepted)

function Main(arg) {
 
    var N = arg.split("\n")[0];
    
    var ans = Number.MAX_SAFE_INTEGER;
    for (var i = 1; i <= Math.sqrt(N); i++){
        if (N % i === 0) {
            var tmp = (i - 1) + (N / i - 1);
            if (ans > tmp) {
                ans = tmp;
            }
        }
    }

    console.log(ans)

    return;
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));