Acdream: Sum

Sumtime limit: 2000/1000 ms (Java/others) memory limit: 128000/64000 KB (Java/others) submitstatisticnext problemproblem description

You are given an N * n digit matrix and you can get several horizontal or vertical digit strings from any position.

For example:

123

456

789

In first row, you can get 6 digit strings totally, which are 23,123.

In first column, you can get 6 digit strings totally, which are 47,147.

We want to get all digit strings from each row and column, and write them on a paper. now I wonder the sum of all number on the paper if we consider a digit string as a complete decimal number.

Input

The first line contains an integer n. (1 <=n <= 1000)

In the next n lines each line contains a string with N digit.

Output

Output the answer after module 1,000,000,007 (1e9 + 7 ).

Sample Input

3123456789

Sample output

2784

The main question is to export the formula:

For example, sum = 1111 for each row of N rows and n columns ..... 111 (N 1) * A1 + 111... 111 (N-1 1) * 2 * A2 + ......... + 11 * (n-1) * an-1 + 1 * n *;

#include<cstdio>#include<cstring>#include<algorithm>#include<iostream>#include<queue>#include<vector>#define M 1000000007#define f1(i, n)  for(int i=1; i<=n; i++)#define f2(i, n)  for(int i=0; i<n; i++)#define f3(j, n)  for(int j=0; j<n; j++)　using namespace std;char a[1050][1050];long long int b[1050];int main(){    int n;    int k=1050;    f1(i, k)       b[i]=0;    f1(i, k)       for(int j=1; j<=i; j++)        b[i]=(b[i]*10+1)%M;    while(~scanf("%d",&n))    {        k=n;        long long int sum=0;        f2(i, k)        {            scanf("%s",&a[i]);           // f3(j, k)           for(int j=0; j<n; j++)                sum=(sum+((((j+1)*((long long)a[i][j]-'0'))*b[n-j])%M))%M;        }        //f3(j, k)        for(int j=0; j<n; j++)        {            f2(i, k)                sum=(sum+((((i+1)*((long long)a[i][j]-'0'))*b[n-i])%M))%M;        }        cout<<sum<<endl;    }    return 0;}