Problem Description
YJQQQAQ has an array A of length n. He defines a function fl,r,k where l,r,k are positive integers that satisfies l≤r and r×k≤n, and the value of the function equals to p×q×⌊k√⌋ where p equals to the sum value of Al×k,A(l+1)×k,...,Ar×k and q equals to the minimal value of them. YJQQQAQ wants to choose the positive integers l,r,k carefully to maximize the value of the function.
Input
The first line contains an integer T(1≤T≤3)——The number of the test cases. For each test case:
The first line contains an integers n(1≤n≤300,000).
The second line contains n integers describing the given array A, the ith integer is Ai(1≤Ai≤1,000,000). Between each two adjacent integers there is a white space separated.
Output
For each test case, the only line contains the only integer that is the maximum value of the function.
Sample Input
1
3
2 3 1
Sample Output
10
