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  
    
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map;
import java.util.NavigableMap;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class a309 {

	static class Task {		
		
		public void Solve(InputReader in, PrintWriter out)
		{
			int n=in.nextInt();
			int arr[]=in.nextIntArray(n);
			int dp[]=new int[n];
			long ans=1;
			dp[0]=arr[0];
			for(int i=1;i<n;i++)
			{
				dp[i]=dp[i-1]+arr[i];
			}
			long bin[][]=new long[1001][1001];
			bin[0][0]=1;
			for(int i=0;i<1001;i++){
				for(int j=0;j<=i;j++){
					if(j==0){
						bin[i][j]=1;
					}
					else if(i==j){
						bin[i][j]=1;
					}
					else{
						bin[i][j]=(bin[i-1][j]+bin[i-1][j-1])%1000000007;
					}
				}
			}
			for(int i=n-1;i>=0;i--)
			{
				ans*=bin[dp[i]-1][arr[i]-1];
				ans=ans%M;
			}
			out.println(ans);
	    }
     }
	
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.Solve(in,out);
        out.close();
    }
  
    static int[][] sort2D(int arr[][]){
        Arrays.sort(arr,new java.util.Comparator<int[]>(){
        public int compare(int[] a, int[] b) {
            return Integer.compare(a[0], b[0]);
        }});
        return arr;
    }
    
    static long M=1000000000+7;
    
	static int[] di={1,0,-1,0,1,-1,-1,1};
	static int[] dj={0,1,0,-1,1,1,-1,-1};
    
	static class point{
		int x;int y;
		public point(int x,int y){
			this.x=x;
			this.y=y;
		}
	}

    static void sort(int arr[]){
		int cnt[]=new int[(1<<16)+1];
		int ys[]=new int[arr.length];	
		for(int j=0;j<=16;j+=16){
			Arrays.fill(cnt,0);
			for(int x:arr){cnt[(x>>j&0xFFFF)+1]++;}
			for(int i=1;i<cnt.length;i++){cnt[i]+=cnt[i-1];}
			for(int x:arr){ys[cnt[x>>j&0xFFFF]++]=x;}
			{ final int t[]=arr;arr=ys;ys=t;}
		}
		if(arr[0]<0||arr[arr.length-1]>=0)return;
		int i,j,c;
		for(i=arr.length-1,c=0;arr[i]<0;i--,c++){ys[c]=arr[i];}
		for(j=arr.length-1;i>=0;i--,j--){arr[j]=arr[i];}
		for(i=c-1;i>=0;i--){arr[i]=ys[c-1-i];}
	}
    
    static int lcm(int a,int b){return a*b/gcd(a,b);}
    static int abs(int x){if(x>=0)return x;else return -x;}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);} 
    static int min(int x,int y){return x<y?x:y;}
    static int min(int x,int y,int z){return x<y?(x<z?x:z):(y<z?y:z);}
    static int max(int x,int y){return x>y?x:y;}
    static int max(int x,int y,int z){return x>y?(x>z?x:z):(y>z?y:z);}
    
    static void joutArray(int arr[]){
    	for(int i=0;i<arr.length;i++){
    		System.out.print(arr[i]+" ");
    	}
    	System.out.println();
    }
    
    static void joutArray(int arr[][],int n,int m){
    	for(int i=0;i<n;i++){
    		for(int j=0;j<m;j++)
    		System.out.print(arr[i][j]+" ");
    		System.out.println();
    	}
    	System.out.println();
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        
        public String nextLine() {
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}

        public int nextInt() {
            return Integer.parseInt(next());
        }
        
        public long nextLong() {
        	return Long.parseLong(next());
        }
        
        public double nextDouble() {
        	return Double.parseDouble(next());
        }
        
        public int[] nextIntArray(int n) {
        	int arr[]=new int[n];
        	for(int i=0;i<n;i++)
        		arr[i]=nextInt();
        	return arr;
        }
        
        public char[] nextCharArray(){
        	char arr[]=next().toCharArray();
        	return arr;
        }
        
        public HashMap<Integer,Integer> inHashMap(int n){
        	HashMap<Integer,Integer> hm=new HashMap<>();
        	for(int i=0;i<n;i++){
    			int num=nextInt();
    			hm.put(num,hm.get(num)==null?1:hm.get(num)+1);
    		}
        	return hm;
        }
     }
    
   }