Farmer Nhoj dropped Bessie in the middle of nowhere! At time $t=0$, Bessie is located at $x=0$ on an infinite number line. She frantically searches for an exit by moving left or right by $1$ unit each second. However, there actually is no exit and after $T$ seconds, Bessie is back at $x=0$, tired and resigned.

Farmer Nhoj tries to track Bessie but only knows how many times Bessie crosses $x=.5,1.5,2.5,…,(N−1).5$, given by an array $A_0,A_1,…,A_{N−1} (1≤N≤10^5, 1≤A_i≤10^6)$. Bessie never reaches $x\gt N$ nor $x\lt 0$.

In particular, Bessie's route can be represented by a string of $T=∑_{i=0}^{N−1}A_i$ $L$s and $R$s where the $i$th character represents the direction Bessie moves in during the $i$th second. The number of direction changes is defined as the number of occurrences of $LR$s plus the number of occurrences of $RL$s.

Please help Farmer Nhoj count the number of routes Bessie could have taken that are consistent with $A$ and minimize the number of direction changes. It is guaranteed that there is at least one valid route.

The first line contains $N$. The second line contains $A_0,A_1,…,A_{N−1}$.

The number of routes Bessie could have taken, modulo $10^9+7$.

Bessie must change direction at least $5$ times. There are two routes corresponding to Bessie changing direction exactly $5$ times:
$$
RRLRLLRRLL \\
RRLLRRLRLL
$$