Rohan is solving a very easy problem but it seems very hard to him. Actually he got a list of n numbers and he has to perform a function on those numbers which is defined as -

$f(a_1,a_2,a_3 . . . . . . a_n) = \sum_{i=1}^n a_i - \sum_{1\le i \lt j \le n }^n g(a_i,a_j) + \sum_{1\le i \lt j \lt k\le n }^n g(a_i,a_j,a_k) - . . . + (-1)^{n-1} g(a_1,a_2,..,a_n)$

Rohan searches the whole internet and finds that the code to the function $g(x,y)$ is available. Also he finds out that for more than two numbers g can be calculated as $g(a,b,c) = g( g(a,b) , g(b,c) )$ and this technique can be used to calculate g for even a list of numbers. So given a list of the numbers can you calculate the function f for Rohan . Algorithm for function $g (x,y)$ is given below -

function g(x,y) {
    if(x-y>0)
        x = x^y^y; // ^ is the xor operator here
    else
        x = x^y^x;// ^ is the xor operator here
    return x;
}