Divisibility by Eight (数学)

Divisibility by Eight

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a non-negative integer n, its decimal representation consists of at most 100 digits and doesn't contain leading zeroes.

Your task is to determine if it is possible in this case to remove some of the digits (possibly not remove any digit at all) so that the result contains at least one digit, forms a non-negative integer, doesn't have leading zeroes and is divisible by 8. After the removing, it is forbidden to rearrange the digits.

If a solution exists, you should print it.

Input

The single line of the input contains a non-negative integer n. The representation of number n doesn't contain any leading zeroes and its length doesn't exceed 100 digits.

Output

Print "NO" (without quotes), if there is no such way to remove some digits from number n.

Otherwise, print "YES" in the first line and the resulting number after removing digits from number n in the second line. The printed number must be divisible by 8.

If there are multiple possible answers, you may print any of them.

Sample test(s)

input

3454

output

YES
344

input

10

output

YES
0

input

111111

output

NO

能被8整除的特性：最后三位可以被8整除。

#include <iostream>
#include <cstdio>
#include <string>
#include <queue>
#include <vector>
#include <map>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <climits>
using    namespace    std;

const    int    SIZE = 105;
char        S[SIZE];
bool        VIS[SIZE],FLAG;
vector<char>    ANS;

void    dfs(int start,int sum,int count);
int    main(void)
{
    cin >> S;
    dfs(0,0,0);
    if(!FLAG)
        puts("NO");

    return    0;
}

void    dfs(int start,int sum,int count)
{
    if(FLAG || count > 3)
        return    ;
    for(int i = start;S[i];i ++)
    {
        if(FLAG)
            return    ;
        if(!VIS[i])
        {
            VIS[i] = true;
            int    back = sum;
            ANS.push_back(S[i]);
            sum = ANS[ANS.size() - 1] - '0';
            if(ANS.size() >= 2)
                sum += (ANS[ANS.size() - 2] - '0') * 10;
            if(ANS.size() >= 3)
                sum += (ANS[ANS.size() - 3] - '0') * 100;
            if(sum % 8 == 0)
            {
                cout << "YES" << endl;
                for(int i = 0;i < ANS.size();i ++)
                    cout << ANS[i];
                cout << endl;
                FLAG = true;
                return    ;
            }

            dfs(i + 1,sum,count + 1);
            VIS[i] = false;
            sum = back;
            ANS.pop_back();
        }
    }
}