A. Disturbing Distribution
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$[a_1, a_2, \ldots, a_n]$$$. You wish to make the array empty by performing the following operation any number of times:

  • Select any sequence of indices $$$1 \le i_1 \lt i_2 \lt \ldots \lt i_k \le |a|$$$ (note that $$$|a|$$$ denotes the current length of the array $$$a$$$) such that $$$$$$a_{i_1} \le a_{i_2} \le \ldots \le a_{i_k}$$$$$$
  • Remove the elements $$$a_{i_1}, a_{i_2}, \ldots, a_{i_k}$$$ from the array $$$a$$$.
  • This operation incurs a cost equal to $$$a_{i_1} \times a_{i_2} \times \cdots \times a_{i_k}$$$.

Determine the minimum total cost required to remove all the elements from the array $$$a$$$. Note that the total cost is equal to the sum of costs incurred over all the operations performed.

As the answer can be very large, report the answer modulo $$$676\,767\,677$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). The description of the test cases follows.

The first line of each testcase contains a single integer $$$n$$$ ($$$1 \le n \le 100$$$) — the length of the array $$$a$$$.

The second line of each testcase contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 100$$$) — the elements of the array.

Output

For each testcase, output a single integer — the minimum total cost required to make the array $$$a$$$ empty.

As the answer may be large, output the answer modulo $$$676\,767\,677$$$.

Example
Input
3
5
1 2 1 2 3
3
3 2 1
4
1 1 1 1
Output
7
6
1
Note

For the first testcase,

  • Operation 1: Choose $$$i_1 = 1$$$, $$$i_2 = 2$$$, and $$$i_3 = 4$$$. This incurs a cost of $$$1 \cdot 2 \cdot 2 = 4$$$. After deleting the elements at these indices, the array becomes $$$a = [1, 3]$$$.

  • Operation 2: Choose $$$i_1 = 1$$$ and $$$i_2 = 2$$$. This incurs a cost of $$$1 \cdot 3 = 3$$$. After deleting the elements at these indices, the array becomes empty.

Thus, the total cost is equal to $$$4 + 3 = 7$$$. It can be shown that this is the minimum possible total cost.