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 $676\,767\,677$.

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.