ACdream: Sum, acdreamsum

ACdream: Sum, acdreamsum

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 *;

Okay .. This writing is still incomplete .. Now, I want to add more information ..

Take the first line 1 2 3 for example ..

1 can only be set by itself, that is, sum + = A1. 2 can have 2, 12. Then sum + = A2 + 10 * A1 + A2; 3 can have 3, 23,123, then:

Sum + = A3 + 10 * A2 + A3 + 100 * A1 + 10 * A2 + a3 ...... sum = 111 * A1 + 11*2 * A2 + 1*3 * A3; that is, the formula mentioned above.

Do not forget to calculate the sum of columns.

#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;}

What is SUM (A2: B34) in Excel?

"-" In sum (G16-I16) is a minus sign... Actually, sum is the same here.
SUM (A2: B34) "A2: B34" refers to all cells in the range of a rectangle from A2 to B34.
= SUM (B22, B23, B34, B35) comma is the symbol used in the function to divide the parameters. Here, we SUM the cells B22, B23, B34, and B35.
* Title
/Division number
$ Absolute reference means that the row number or column number behind $ will not change when dragging and filling

What is SUM (B: B) in Excel?

SUM (B: B) sums the values of Column B.
If SUM (A: B) is used, the AB column is summed.
If SUM (A1: B10) is used, it is used to SUM the rectangular area of the 10 rows in the two columns of A1: B10.

However, if the SUM is only for Column B, it cannot be written as SUM (B) or SUM (B: B), which references the entire column; or SUM (B1: B100, reference area.

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