Problem Statement

There are $N$ coins, numbered from $1$ to $N$.
Because these coins have special shapes, when the $i$-th coin is tossed at random, the probability of landing heads is $\displaystyle{\frac{P_i}{100}}$ and the probability of landing tails is $\displaystyle{\frac{100-P_i}{100}}$.

Alice and Bob choose $1$ or more coins from among these and play the following game.

• Toss all the chosen coins at random.
• If the number of coins that landed heads is odd, Alice wins; if it is even, Bob wins.

There are $2^N-1$ ways to choose the coins. Among them, how many ways make the probability of Alice winning strictly greater than $1/2$?
Since the answer can be very large, output it modulo $10^9+7$.

Input

$N$
$P_1\ \ P_2\ \ \cdots\ \ P_N$

• $1\le N\le 100$
• $0\le P_i \le 100$
• All inputs are integers.

Output

Output the number of ways to choose the coins such that the probability of Alice winning is strictly greater than $1/2$, modulo $10^9+7$.

Sample

2
30 80

2

1
50

0