Codeforces 383D. Antimatter DP, codeforces383d

Codeforces 383D. Antimatter DP, codeforces383d

D. Antimattertime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output

Iahub accidentally discovered a secret lab. He found thereNDevices ordered in a line, numbered from 1NFrom left to right. Each deviceI(1 digit ≤ DigitILimit ≤ limitN) Can create eitherAIUnits of matter orAIUnits of antimatter.

Iahub wants to choose some contiguous subarray of devices in the lab, specify the production mode for each of them (produce matter or antimatter) and finally take a photo of it. however he will be successful only if the amounts of matter and antimatter produced in the selected subarray will be the same (otherwise there wocould be overflowing matter or antimatter in the photo ).

You are requested to compute the number of different ways Iahub can successful take a photo. A photo is different than another if it represents another subarray, or if at least one device of the subarray is set to produce matter in one of the photos and antimatter in the other one.

Input

The first line contains an integerN(1 digit ≤ DigitNLimit ≤00001000). The second line containsNIntegersA1,A2 ,...,AN(1 digit ≤ DigitAILimit ≤ limit 1000 ).

The sumA1 worker + workerA2 cores + cores... cores + CoresANWill be less than or equal to 10000.

Output

Output a single integer, the number of ways Iahub can take a photo, modulo 1000000007 (109 bytes + snapshot 7 ).

Sample test (s) input

41 1 1 1

Output

12

Note

The possible photos are [1 +, 2-], [1-, 2 +], [2 +, 3-], [2-, 3 +], [3 +, 4-], [3-, 4 +], [1 +, 2 +, 3-, 4-], [1 +, 2-, 3 +, 4-], [1 +, 2-, 3-, 4 +], [1-, 2 +, 3 +, 4-], [1-, 2 +, 3 -, 4 +] and [1-, 2-, 3 +, 4 +], where"I+ "Means thatI-Th element produces matter, and"I-"Means thatI-Th element produces antimatter.

import java.util.*;public class CF383D{        final int MOD = 1000000007;    final int BASE = 10010;    int[] a = new int[1111];    int n,sum=0;    int[][] dp = new int[1111][21111];        CF383D(){        Scanner in = new Scanner(System.in);        n=in.nextInt();        for(int i=1;i<=n;i++){            a[i]=in.nextInt();            sum+=a[i];        }                dp[0][BASE]=1;                for(int i=1;i<=n;i++)        {            dp[i][BASE]=1;            for(int j=-sum;j<=sum;j++)            {                if(dp[i-1][j+BASE]!=0)                {                    dp[i][j+BASE+a[i]]+=dp[i-1][j+BASE];                    dp[i][j+BASE+a[i]]%=MOD;                    dp[i][j+BASE-a[i]]+=dp[i-1][j+BASE];                    dp[i][j+BASE-a[i]]%=MOD;                }            }        }        int ans=0;        for(int i=1;i<=n;i++)        {            ans+=dp[i][BASE]-1;            ans%=MOD;        }                System.out.println(ans);    }        public static void main(String[] args){        new CF383D();    }}