### 题目描述

``````
7
3   8
8   1   0
2   7   4   4
4   5   2   6   5

(Figure 1)``````

Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.

### 输入

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.

### 输出

Your program is to write to standard output. The highest sum is written as an integer.

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

30

### 代码如下

``````import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner s = new Scanner(System.in);
int n=s.nextInt();

int [][] a=new int [n+1][n+1];
int [][] maxsum=new int [n+1][n+1];
int i,j;
for( i=1;i<=n;i++){
for( j=1;j<=i;j++){
a[i][j]=s.nextInt();
}
}
for( i=1;i<=n;i++){
maxsum[n][i]=a[n][i];
}
for(i=n-1;i>0;i--){
for( j=1;j<=i;j++){
maxsum[i][j]=Math.max(maxsum[i+1][j],maxsum[i+1][j+1])+a[i][j];
}
}
System.out.println(maxsum);
}
}
``````