You've got array a[1],a[2],...,a[n], consisting of n integers. Count the number of ways to split all the elements of the array into three contiguous parts so that the sum of elements in each part is the same.

More formally, you need to find the number of such pairs of indices i,j (2 \le i \le j \le n-1), that .

The first line contains integer n (1 \le n \le 5 \cdot 105), showing how many numbers are in the array. The second line contains n integers a[1], a[2], ..., a[n] (|a[i]| \le 109) - the elements of array a.

Print a single integer - the number of ways to split the array into three parts with the same sum.