문제

The grass has dried up in Farmer John's pasture due to a drought. After hours of despair and contemplation, FJ comes up with the brilliant idea of purchasing corn to feed his precious cows.

FJ’s $N$ ($1 \leq N \leq 100$) cows are arranged in a line such that the $i$th cow in line has a non-negative integer hunger level of $h_i$. As FJ’s cows are social animals and insist on eating together, the only way FJ can decrease the hunger levels of his cows is to select two adjacent cows $i$ and $i+1$ and feed each of them a bag of corn, causing each of their hunger levels to decrease by one.

FJ wants to feed his cows until all of them have the same non-negative hunger level. Although he doesn't know his cows' exact hunger levels, he does know an upper bound on the hunger level of each cow; specifically, the hunger level $h_i$ of the $i$-th cow is at most $H_i$ ($0\le H_i\le 1000$).

Your job is to count the number of $N$-tuples of hunger levels $[h_1,h_2,\ldots,h_N]$ that are consistent with these upper bounds such that it is possible for FJ to achieve his goal, modulo $10^9+7$.

입력

The first line contains $N$.

The second line contains $H_1,H_2,\ldots,H_N$.

출력

The number of $N$-tuples of hunger levels modulo $10^9+7$.

예제 입력 1

3
9 11 7

예제 출력 1

241

예제 입력 2

4
6 8 5 9

예제 출력 2

137

점수

$N$ is even in even-numbered tests and odd in odd-numbered tests.

Tests 3 and 4 satisfy $N\le 6$ and $H_i \le 10$.Tests 5 through 10 satisfy $N\le 50$ and $H_i \le 100$.Tests 11 through 20 satisfy no further constraints.