27557번 - Moo Route 다국어

문제

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

Farmer Nhoj tries to track Bessie but only knows how many times Bessie crosses $x=.5, 1.5, 2.5, \ldots, (N-1).5,ドル given by an array $A_0,A_1,\dots,A_{N-1}$ (1ドル\leq N \leq 10^5,ドル 1ドル \leq A_i \leq 10^6$). Bessie never reaches $x>N$ nor $x<0$.

In particular, Bessie's route can be represented by a string of $T = \sum_{i=0}^{N-1} A_i$ $L$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.

입력

The first line contains $N$. The second line contains $A_0,A_1,\dots,A_{N-1}$.

출력

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

제한

힌트

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

RRLRLLRRLL
RRLLRRLRLL