550C. Divisibility by Eight

Brute force, dp, math, 1500, https://codeforces.com/contest/550/problem/C

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.

Examples

input

3454

output

YES
344

input

10

output

YES
0

input

111111

output

NO

记忆式搜索，20-21是分叉。

'''
应该递归后三位，而不是所有的位数。因为
A number is divisible by 8 if its last three digits are also divisible by 8
'''
from functools import lru_cache

@lru_cache(maxsize=None)
def dfs(n, i, depth):
    global bo, result
    if depth > 3 or bo:
        return
    if len(n) > 0 and int(n) % 8 == 0:
        result = n
        bo = True
        return
    if bo:
        return
    if i >= l:
        return
    dfs(n, i+1, depth)
    dfs(n+s[i], i+1, depth+1)


s = input()
l = len(s)
bo = False
result = ""
dfs('', 0, 0)
if bo:
    print('YES\n', result)
else:
    print('NO')

Brute force

def check_divisibility_by_8(n):
    # A number is divisible by 8 if its last three digits are also divisible by 8
    
    # Check for single and double digit cases
    if int(n) % 8 == 0:
        return ("YES", n)
    for i in range(len(n)):
        if int(n[i]) % 8 == 0:
            return ("YES", n[i])
        for j in range(i + 1, len(n)):
            if int(n[i] + n[j]) % 8 == 0:
                return ("YES", n[i] + n[j])
            for k in range(j + 1, len(n)):
                if int(n[i] + n[j] + n[k]) % 8 == 0:
                    return ("YES", n[i] + n[j] + n[k])
    # If no divisibility by 8 found
    return ("NO",)
 
 
#inputs = ["3454","10","111111"]
 
 
#for number in inputs:
number = input()
result = check_divisibility_by_8(number)
if result[0] == "YES":
    print(result[0])
    print(result[1])
else:
    print(result[0])