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

#include <bits/stdc++.h>
using namespace std;
class BigNum {
 private:
  int a[50000];
  int len;

 public:
  BigNum() {
    len = 1;
    memset(a, 0, sizeof(a));
  }
  BigNum(const int);
  BigNum(const char *);
  BigNum(const BigNum &);
  BigNum &operator=(const BigNum &);
  friend istream &operator>>(istream &, BigNum &);
  friend ostream &operator<<(ostream &, BigNum &);
  BigNum operator+(const BigNum &) const;
  BigNum operator-(const BigNum &) const;
  BigNum operator*(const BigNum &) const;
  BigNum operator/(const int &) const;
  BigNum operator^(const int &) const;
  int operator%(const int &) const;
  bool operator>(const BigNum &T) const;
  bool operator>(const int &t) const;
  void print();
};
BigNum::BigNum(const int b) {
  int c, d = b;
  len = 0;
  memset(a, 0, sizeof(a));
  while (d > 9999) {
    c = d - (d / (9999 + 1)) * (9999 + 1);
    d = d / (9999 + 1);
    a[len++] = c;
  }
  a[len++] = d;
}
BigNum::BigNum(const char *s) {
  int t, k, index, l, i;
  memset(a, 0, sizeof(a));
  l = strlen(s);
  len = l / 4;
  if (l % 4) len++;
  index = 0;
  for (i = l - 1; i >= 0; i -= 4) {
    t = 0;
    k = i - 4 + 1;
    if (k < 0) k = 0;
    for (int j = k; j <= i; j++) t = t * 10 + s[j] - '0';
    a[index++] = t;
  }
}
BigNum::BigNum(const BigNum &T) : len(T.len) {
  int i;
  memset(a, 0, sizeof(a));
  for (i = 0; i < len; i++) a[i] = T.a[i];
}
BigNum &BigNum::operator=(const BigNum &n) {
  int i;
  len = n.len;
  memset(a, 0, sizeof(a));
  for (i = 0; i < len; i++) a[i] = n.a[i];
  return *this;
}
istream &operator>>(istream &in, BigNum &b) {
  char ch[10 * 4];
  int i = -1;
  in >> ch;
  int l = strlen(ch);
  int count = 0, sum = 0;
  for (i = l - 1; i >= 0;) {
    sum = 0;
    int t = 1;
    for (int j = 0; j < 4 && i >= 0; j++, i--, t *= 10) {
      sum += (ch[i] - '0') * t;
    }
    b.a[count] = sum;
    count++;
  }
  b.len = count++;
  return in;
}
ostream &operator<<(ostream &out, BigNum &b) {
  int i;
  cout << b.a[b.len - 1];
  for (i = b.len - 2; i >= 0; i--) {
    cout.width(4);
    cout.fill('0');
    cout << b.a[i];
  }
  return out;
}
BigNum BigNum::operator+(const BigNum &T) const {
  BigNum t(*this);
  int i, big;
  big = T.len > len ? T.len : len;
  for (i = 0; i < big; i++) {
    t.a[i] += T.a[i];
    if (t.a[i] > 9999) {
      t.a[i + 1]++;
      t.a[i] -= 9999 + 1;
    }
  }
  if (t.a[big] != 0)
    t.len = big + 1;
  else
    t.len = big;
  return t;
}
BigNum BigNum::operator-(const BigNum &T) const {
  int i, j, big;
  bool flag;
  BigNum t1, t2;
  if (*this > T) {
    t1 = *this;
    t2 = T;
    flag = 0;
  } else {
    t1 = T;
    t2 = *this;
    flag = 1;
  }
  big = t1.len;
  for (i = 0; i < big; i++) {
    if (t1.a[i] < t2.a[i]) {
      j = i + 1;
      while (t1.a[j] == 0) j++;
      t1.a[j--]--;
      while (j > i) t1.a[j--] += 9999;
      t1.a[i] += 9999 + 1 - t2.a[i];
    } else
      t1.a[i] -= t2.a[i];
  }
  t1.len = big;
  while (t1.a[len - 1] == 0 && t1.len > 1) {
    t1.len--;
    big--;
  }
  if (flag) t1.a[big - 1] = 0 - t1.a[big - 1];
  return t1;
}
BigNum BigNum::operator*(const BigNum &T) const {
  BigNum ret;
  int i, j, up;
  int temp, temp1;
  for (i = 0; i < len; i++) {
    up = 0;
    for (j = 0; j < T.len; j++) {
      temp = a[i] * T.a[j] + ret.a[i + j] + up;
      if (temp > 9999) {
        temp1 = temp - temp / (9999 + 1) * (9999 + 1);
        up = temp / (9999 + 1);
        ret.a[i + j] = temp1;
      } else {
        up = 0;
        ret.a[i + j] = temp;
      }
    }
    if (up != 0) ret.a[i + j] = up;
  }
  ret.len = i + j;
  while (ret.a[ret.len - 1] == 0 && ret.len > 1) ret.len--;
  return ret;
}
BigNum BigNum::operator/(const int &b) const {
  BigNum ret;
  int i, down = 0;
  for (i = len - 1; i >= 0; i--) {
    ret.a[i] = (a[i] + down * (9999 + 1)) / b;
    down = a[i] + down * (9999 + 1) - ret.a[i] * b;
  }
  ret.len = len;
  while (ret.a[ret.len - 1] == 0 && ret.len > 1) ret.len--;
  return ret;
}
int BigNum::operator%(const int &b) const {
  int i, d = 0;
  for (i = len - 1; i >= 0; i--) {
    d = ((d * (9999 + 1)) % b + a[i]) % b;
  }
  return d;
}
BigNum BigNum::operator^(const int &n) const {
  BigNum t, ret(1);
  int i;
  if (n < 0) exit(-1);
  if (n == 0) return 1;
  if (n == 1) return *this;
  int m = n;
  while (m > 1) {
    t = *this;
    for (i = 1; i << 1 <= m; i <<= 1) {
      t = t * t;
    }
    m -= i;
    ret = ret * t;
    if (m == 1) ret = ret * (*this);
  }
  return ret;
}
bool BigNum::operator>(const BigNum &T) const {
  int ln;
  if (len > T.len)
    return true;
  else if (len == T.len) {
    ln = len - 1;
    while (a[ln] == T.a[ln] && ln >= 0) ln--;
    if (ln >= 0 && a[ln] > T.a[ln])
      return true;
    else
      return false;
  } else
    return false;
}
bool BigNum::operator>(const int &t) const {
  BigNum b(t);
  return *this > b;
}
void BigNum::print() {
  int i;
  cout << a[len - 1];
  for (i = len - 2; i >= 0; i--) {
    cout.width(4);
    cout.fill('0');
    cout << a[i];
  }
  cout << endl;
}
int main() {
  int color;
  int s[1005];
  while (scanf("%d", &color) == 1) {
    int sum = 0;
    for (int i = 0; i < color; i++) {
      scanf("%d", &s[i]);
      sum += s[i];
    }
    s[color - 1]--;
    s[color - 2]--;
    BigNum t = 1, x = 1;
    for (int i = 1; i <= sum - 2; i++) t = t * i;
    for (int i = 0; i < color; i++) {
      for (int j = 2; j <= s[i]; j++) {
        t = t / j;
      }
    }
    t = t % 1000000007;
    t.print();
  }
  return 0;
}
