Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

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

process.stdin.resume();
process.stdin.setEncoding('utf8');

var g_input = '';
process.stdin.on('data', function(chunk) {
    g_input += chunk;
});

process.stdin.on('end', function() {
    Main(g_input.split(/\r?\n/));
});

function Main(input) {
    var capitalN = parseInt(input[0], 10);
    var h = 0;
    var n = 0;
    var w = 0;

    var a = 4 / capitalN;
    var b = 2 / 3500;
    var c = 1 / 3500;

    var isFound = false;
//    console.log(Math.floor(1 / (a - b)));
//    for (h = Math.floor(1 / (a - b)); h < 3500; h++) {
    for (h = 1; h <= 3500; h++) {

//        if (a < 1 / h + b) {
//            continue;
//        }

//        console.log(Math.floor(1 / (a - 1 / h - c)));
//        for (n = Math.floor(1 / (a - 1 / h - c)); n < 3500; n++) {
        for (n = h; n <= 3500; n++) {

//            if (a < 1 / h + 1 / n + c) {
//                continue;
//            }

            if (4 * h * n - capitalN * h - capitalN * n != 0) {
                w = Math.ceil((capitalN * h * n) / (4 * h * n - capitalN * h - capitalN * n));
            //for (w = n; w < 3500; w++) {

                if (w > 0 && a === 1 / h + 1 / n + 1 / w) {
                    isFound = true;
                    break;
                }
            //}
            }

            if (isFound) {
                break;
            }
        }

        if (isFound) {
            break;
        }
    }

    console.log(h + ' ' + n + ' ' + w);

    return 0;
}