Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Kyoya and Colored Balls

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputKyoya Ootori has a bag with *n* colored balls that are colored with *k* different colors. The colors are labeled from 1 to *k*. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color *i* before drawing the last ball of color *i* + 1 for all *i* from 1 to *k* - 1. Now he wonders how many different ways this can happen.

Input

The first line of input will have one integer *k* (1 ≤ *k* ≤ 1000) the number of colors.

Then, *k* lines will follow. The *i*-th line will contain *c*_{i}, the number of balls of the *i*-th color (1 ≤ *c*_{i} ≤ 1000).

The total number of balls doesn't exceed 1000.

Output

A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007.

Examples

Input

3

2

2

1

Output

3

Input

4

1

2

3

4

Output

1680

Note

In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are:

1 2 1 2 3

1 1 2 2 3

2 1 1 2 3

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/18/2020 20:45:47 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|