Let's denote d(n) as the number of divisors of a positive integer n. You are given three integers a, b and c. Your task is to calculate the following sum:

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Find the sum modulo 1073741824 (230).

Input

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Examples

Input

2 2 2


Output

20


Input

5 6 7


Output

1520

Note

For the first example.

  * d(1·1·1) = d(1) = 1; 
  * d(1·1·2) = d(2) = 2; 
  * d(1·2·1) = d(2) = 2; 
  * d(1·2·2) = d(4) = 3; 
  * d(2·1·1) = d(2) = 2; 
  * d(2·1·2) = d(4) = 3; 
  * d(2·2·1) = d(4) = 3; 
  * d(2·2·2) = d(8) = 4. 



So the result is 1 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 20.
// http://codeforces.com/contest/236/problem/B

var memObj = {};
function d(n) {
    var num = 0;
    if (memObj[n]) {
        num = memObj[n];
    } else {
        if (n == 1) return 1;
        num = 2;
        var k = Math.floor(Math.sqrt(n));
        for (var i = 2; i <= k; i++) {
            if (n%i === 0) {
                num += 2;
            }

            if (i*i ==n ) num --;
        }
        memObj[n] = num;
    }

    return num;
}

function getSum(a,b,c) {
    var sum = 0;
    for (var i = 1; i <= a; i++) {
        for (var j = 1; j <= b; j++) {
            for (var k =1; k <= c; k++) {
                sum += d(i*j*k);
            }
        }
    }

    return sum;
}

var args = readline().split(' ');
print(getSum(args[0], args[1], args[2])%1073741824);
