Problem Statement

There are $N$ buildings under construction arranged in a row, numbered $1, 2, \\ldots, N$ from left to right.

Given is an integer sequence $X$ of length $N$. The height of Building $i$, $H_i$, can be one of the integers between $1$ and $X_i$ (inclusive).

For each $i$ such that $1 \\leq i \\leq N$, let us define $P_i$ as follows:

• If there is an integer $j (1 \\leq j < i)$ such that $H_j > H_i$, $P_i$ is the maximum such $j$. Otherwise, $P_i$ is $\-1$.

Considering all possible combinations of the buildings' heights, find the number of integer sequences that $P$ can be, modulo $1000000007$.

Constraints

• $1 \\leq N \\leq 100$
• $1 \\leq X_i \\leq 10^5$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$N$ $X_1$ $X_2$ $\\cdots$ $X_N$

Output

Print the number of integer sequences that $P$ can be when all possible combinations of the buildings' heights are considered, modulo $1000000007$.

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Sample Input 1

3
3 2 1

Sample Output 1

4

We have six candidates for $H$, as follows:

• $H = (1, 1, 1)$, for which $P$ is $(-1, -1, -1)$;
• $H = (1, 2, 1)$, for which $P$ is $(-1, -1, 2)$;
• $H = (2, 1, 1)$, for which $P$ is $(-1, 1, 1)$;
• $H = (2, 2, 1)$, for which $P$ is $(-1, -1, 2)$;
• $H = (3, 1, 1)$, for which $P$ is $(-1, 1, 1)$;
• $H = (3, 2, 1)$, for which $P$ is $(-1, 1, 2)$.

Thus, there are four integer sequences that $P$ can be: $(-1, -1, -1), (-1, -1, 2), (-1, 1, 1)$, and $(-1, 1, 2)$.

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Sample Input 2

3
1 1 2

Sample Output 2

1

We have two candidates for $H$, as follows:

• $H = (1, 1, 1)$, for which $P$ is $(-1, -1, -1)$;
• $H = (1, 1, 2)$, for which $P$ is $(-1, -1, -1)$.

Thus, there is one integer sequence that $P$ can be.

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Sample Input 3

5
2 2 2 2 2

Sample Output 3

16

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Sample Input 4

13
3 1 4 1 5 9 2 6 5 3 5 8 9

Sample Output 4

31155