A834.Drought--Gold

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鈥檚 $N$ ($1 \leq N \leq 100$) 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鈥檚 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 $10^9+7$.

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

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

There are $(9+1)\cdot (11+1)\cdot (7+1)$ $3$-tuples $h$ that are consistent
with $H$.
One of these tuples is $h=[8,10,5]$. In this case, it is possible to make all
cows have equal hunger values: give two bags of corn to both cows $2$ and $3$,
then give five bags of corn to both cows $1$ and $2$, resulting in each cow
having a hunger level of $3$.
Another one of these tuples is $h=[0,1,0]$. In this case, it is impossible to
make the hunger levels of the cows equal.