有一道算法题，不知各位能否帮我看看错在哪里？

[zxhseu]

Background

The digital root of a positive integer is found by summing the digits of the integer. If the resulting value is a single digit then that digit is the digital root. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as long as necessary to obtain a single digit.

For example, consider the positive integer 24. Adding the 2 and the 4 yields a value of 6. Since 6 is a single digit, 6 is the digital root of 24. Now consider the positive integer 39. Adding the 3 and the 9 yields 12. Since 12 is not a single digit, the process must be repeated. Adding the 1 and the 2 yeilds 3, a single digit and also the digital root of 39.


Input

The input file will contain a list of positive integers, one per line. The end of the input will be indicated by an integer value of zero.


Output

For each integer in the input, output its digital root on a separate line of the output.


Example

Input



24
39
0
Output

6
3

意思就是说算一个正整数各位的和，如果答案不是一位数，就继续算下去，直到结果是一位数为止。

以下是我写的代码（C＋＋）
#include<iostream.h>

int digit(int &num)
{
int result = num;
while(result>9)
{
result = 0;
while(num>9)
{
result += num%10;
num = num/10;
}
result += num;
num = result;
}
return result;
}


int main()
{
int n,i;
int *data = new int[100];
int *result = new int[100];

cout<<"Please input several positive integers, one per line, \nended by an integer value of zero："<<endl;

for(i=0;;i++)
{
cin>>data[i];
if(!data[i])
{
n=i;
break;
}
}

cout<<"The output: their digital roots:"<<endl;

for(i=0; i<n; i++)
{
result[i] = digit(data[i]);
cout<<result[i]<<endl;
}

delete []data;
delete []result;
return 0;
}


自己觉得没什么错误，但交到在线答题系统里，说我的是wrong answer，为什么啊？

[gxqcn]

也许这样更快：
int digit(int &num)
{
　　return num % 9;
}

[mmmcd]

把这些多余的输出都删掉
cout<<"Please input several positive integers, one per line, \nended by an integer value of zero："<<endl;
...

cout<<"The output: their digital roots:"<<endl;

[zxhseu]

这样不对，并不是让你计算结果是否能被9整除啊
如果能被9整除，答案是应该是9，而不是0
而且就算这样，我的也不会是算法错误啊

[zxhseu]

回复人： mmmcd(超超) ( ) 信誉：124 2006-02-13 17:17:00 得分: 0


把这些多余的输出都删掉
cout<<"Please input several positive integers, one per line, \nended by an integer value of zero："<<endl;
...

cout<<"The output: their digital roots:"<<endl;


去掉了似乎还是不对

[gxqcn]

unsigned int digit(unsigned int num)
{
return ( 0 == num ) ? 0 : (( num - 1 ) % 9 ) + 1;
}

注意：去掉你原有的 digit(..) 入参“&”引用试试（用我上面改写的代码，加不加引用“&”均可）。