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

/* Author : DEBOJYOTI MANDAL
Attribute : Some of the methods are copied from GeeksforGeeks Website  */
import java.util.*;
import java.lang.*;
import java.io.*;
public class Main
{ 
  static  Reader sc=new Reader();
  // static FastReader sc=new FastReader(System.in);
  static long mod=(long)1e9+7;
  static long binomialCoeff(long n, long r)
{
 
    if (r > n)
    return 0;
    long  m = 1000000007;
    long  inv[] = new long[(int)r + 1];
    inv[0] = 1;
    if(r+1>=2)
    inv[1] = 1;
 
    // Getting the modular inversion
    // for all the numbers
    // from 2 to r with respect to m
    // here m = 1000000007
    for (int i = 2; i <= r; i++) {
        inv[i] = m - (m / i) * inv[(int) (m % i)] % m;
    }
 
    long ans = 1;
 
    // for 1/(r!) part
    for (int i = 2; i <= r; i++) {
        ans = (int) (((ans % m) * (inv[i] % m)) % m);
    }
 
    // for (n)*(n-1)*(n-2)*...*(n-r+1) part
    for (long i = n; i >= (n - r + 1); i--) {
        ans = (int) (((ans % m) * (i % m)) % m);
    }
    return ans;
}
 public static void main (String[] args) throws java.lang.Exception
   {
//	try{
	    /*
	        int n=sc.nextInt();
	        ArrayList<Integer> al=new ArrayList<>();
	        ArrayList<Long> al=new ArrayList<>();
	        Set<Integer> set=new HashSet<>();
	        Collections.sort(al,Collections.reverseOrder());
	     
	        long n=sc.nextLong();
	        for(int i=0;i<n;i++) 
	        String s=sc.next();
	     */
		  int t =1;// sc.nextInt();
		  while(t-->0)
		    { 
		       int n=sc.nextInt();
		       
		       int a[]=new int[n];
		       for(int i=0;i<n;i++)
		         {
		           a[i]=sc.nextInt();
		         }
		       long ans=1;
		       long total=0;
		       for(int i=0;i<n;i++)
		         {
		            long res=binomialCoeff(total+a[i]-1,a[i]-1);
		            ans=(ans*res%mod)%mod;
		            total+=a[i];
		            
		            if(total>=mod)
		             total%=mod;
		         }
		      
		      out.println(ans);
		    }
	     out.flush();
	     out.close();
// 	   }     
// 	catch(Exception e)
// 		 {}
	}
 
 /*
   ...SOLUTION ENDS HERE...........SOLUTION ENDS HERE...
 */
 
static void flag(boolean flag)
   {
       out.println(flag ? "YES" : "NO");
       out.flush();
   }
   
 /*                     
    Map<Long,Long> map=new HashMap<>();
             for(int i=0;i<n;i++)
               {
                  if(!map.containsKey(a[i]))
                   map.put(a[i],1);
                 else
                   map.replace(a[i],map.get(a[i])+1);
               }
     
    Set<Map.Entry<Long,Long>> hmap=map.entrySet();
             for(Map.Entry<Long,Long> data : hmap)
               {
          
               }
       
   Iterator<Integer> it = set.iterator();
          while(it.hasNext()) 
           { 
            int x=it.next();
           }
   */

static void print(int a[])
  {
     int n=a.length;
     for(int i=0;i<n;i++)
       {
          out.print(a[i]+" ");
       }
     out.println();
     out.flush();
  }
static void print(long a[])
  {
     int n=a.length;
     for(int i=0;i<n;i++)
       {
          out.print(a[i]+" ");
       }
     out.println();
     out.flush();
  } 
static void print_int(ArrayList<Integer> al)
  {
     int si=al.size();
     for(int i=0;i<si;i++)
       {
          out.print(al.get(i)+" ");
       }
     out.println();
     out.flush();
  }
static void print_long(ArrayList<Long> al)
  {
     int si=al.size();
     for(int i=0;i<si;i++)
       {
          out.print(al.get(i)+" ");
       }
     out.println();
     out.flush();
  }

static class Graph
  {
        int v;
        ArrayList<Integer> list[];
        Graph(int v)
        {
            this.v=v;
            list=new ArrayList[v+1];
            for(int i=1;i<=v;i++)
                list[i]=new ArrayList<Integer>();
        }
        void addEdge(int a, int b)
        {
            this.list[a].add(b);
        }
    }
static void DFS(Graph g, boolean[] visited, int u)
	{
        visited[u]=true;
        int v=0;
        for(int i=0;i<g.list[u].size();i++)
        {
            v=g.list[u].get(i);
            if(!visited[v])
               DFS(g,visited,v);
        }
  } 
  
// static class Pair
//    {
//       int x,y;
//       Pair(int x,int y)
//        {
//           this.x=x;
//           this.y=y;
//        }
//    }
   
static long sum_array(int a[])
 {
    int n=a.length;
    long sum=0;
    for(int i=0;i<n;i++)
     sum+=a[i];
    return sum;
 }
static long sum_array(long a[])
 {
    int n=a.length;
    long sum=0;
    for(int i=0;i<n;i++)
     sum+=a[i];
    return sum;
 }

 static void sort(int[] a) 
   {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
static void sort(long[] a) 
   {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

static void reverse_array(int a[])
 {
    int n=a.length;
    int i,t; 
    for (i = 0; i < n / 2; i++) { 
            t = a[i]; 
            a[i] = a[n - i - 1]; 
            a[n - i - 1] = t; 
        } 
 }
static void reverse_array(long a[])
 {
    int n=a.length;
    int i; long t; 
    for (i = 0; i < n / 2; i++) { 
            t = a[i]; 
            a[i] = a[n - i - 1]; 
            a[n - i - 1] = t; 
        } 
 }
 
static long gcd(long a, long b) 
    { 
        if (a == 0) 
            return b; 
          
        return gcd(b%a, a); 
    } 
static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
          
        return gcd(b%a, a); 
    } 

   static class FastReader{
 
        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;
 
        FastReader(InputStream is) {
            in = is;
        }
 
        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }
 
        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan());
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }
 
        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
 
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
   
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
  static  PrintWriter out=new PrintWriter(System.out);
  static int int_max=Integer.MAX_VALUE;
  static int int_min=Integer.MIN_VALUE;
  static long long_max=Long.MAX_VALUE;
  static long long_min=Long.MIN_VALUE;
}
// Thank You !