Let's call a sequence of integers a1, a2, ..., aN _almost monotonic_ if first
K elements are non-decreasing sequence and last N-K+1 elements are non-
increasing sequence: a1≤a2≤...≤aK and aK≥aK+1≥...≥aN.

The _diversity number_ of a sequence a1, a2, ..., aN is the number of possible
sequences b1, b2,..., bN for which 0≤bi<ai and all of the numbers b1, b2,...,
bN are different. The diversity number of an empty sequence is 1.

You need to find the sum of the diversity numbers of all almost monotonic
subsequences of a sequence. Since this number can be very large, find it
modulo 1,000,000,007. A subsequence is a sequence that can be obtained from
another sequence by deleting some elements without changing the order of the
remaining elements. Two sequences are considered different if their lengths
differ or there is at least one position at which they differ.

## Input

The first line of the input file consists of a single number **T**, the number
of test cases. Each test case consists of a number **M**, the number of
elements in a sequence, followed by **M** numbers **n**, elements of some
sequence (note that this sequence is not necessarily _almost monotonic_). All
tokens are whitespace-separated

## Constraints

**T** = 20  
1 ≤ **M**, **n** ≤ 100

## Output

Output T lines, with the answer to each test case on a single line.