Time Limit: / MS (Java/Others)    Memory Limit: / K (Java/Others)

Total Submission(s):     Accepted Submission(s): 

Problem Description

In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two nodes are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.

You find a partial tree on the way home. This tree has n nodes but lacks of n− edges. You want to complete this tree by adding n− edges. There must be exactly one path between any two nodes after adding. As you know, there are nn− ways to complete this tree, and you want to make the completed tree as cool as possible. The coolness of a tree is the sum of coolness of its nodes. The coolness of a node is f(d), where f is a predefined function and d is the degree of this node. What's the maximum coolness of the completed tree?

Input

The first line contains an integer T indicating the total number of test cases.

Each test case starts with an integer n in one line,

then one line with n− integers f(),f(),…,f(n−).

≤T≤

≤n≤

≤f(i)≤

There are at most  test cases with n>.

Output

For each test case, please output the maximum coolness of the completed tree in one line.

Sample Input

Sample Output

Source

2015ACM/ICPC亚洲区长春站-重现赛（感谢东北师大）

Recommend

hujie