Kyoya 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 ci, the number of balls of the i-th color (1 ≤ ci ≤ 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  
    
25
35
43
38
33
47
44
40
36
41
42
33
30
49
42
62
39
40
35
43
31
42
46
42
34
33
 47
20
21
16
18
24
20
25
13
20
22
26
24
17
18
21
22
21
23
17
15
24
19
18
21
20
19
26
25
20
17
17
17
26
32
20
21
25
28
24
21
21
17
28
20
20
31
19
 3
343
317
337
 1
5
 10
100
100
100
100
100
100
100
100
100
100
 1
1
 13
67
75
76
80
69
86
75
86
81
84
73
72
76
 5
10
10
10
10
10
 11
291
381
126
39
19
20
3
1
20
45
2

362689152
 295545118
 691446102
 1
 12520708
 1
 232242896
 425711769
 902382672

"""
#If FastIO not needed, used this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""

import os
import sys
from io import BytesIO, IOBase
import heapq as h 
from bisect import bisect_left, bisect_right

from types import GeneratorType
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        import os
        self.os = os
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            self.os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")

from collections import defaultdict as dd, deque as dq
import math, string

def getInts():
    return [int(s) for s in input().split()]

def getInt():
    return int(input())

def getStrs():
    return [s for s in input().split()]

def getStr():
    return input()

def listStr():
    return list(input())

MOD = 10**9+7

"""
Number of ways to position ith ball is (C1+C2+...+Ci - 1) choose (Ci - 1)


"""
facs = [1]
curr = 1
for j in range(1,10**6+1):
    curr *= j
    curr %= MOD
    facs.append(curr)

def solve():
    N = getInt()
    cols = []
    pref = []
    curr = 0
    for i in range(N):
        x = getInt()
        curr += x
        cols.append(x)
        pref.append(curr)
    dp = 1
    for j in range(1,N):
        tot = pref[j]
        mult = facs[tot-1]*pow(facs[cols[j]-1], MOD-2, MOD)*pow(facs[pref[j-1]],MOD-2,MOD)
        dp *= mult
        dp %= MOD
    return dp
    
    
#for _ in range(getInt()):
print(solve())