Polycarp likes numbers that are divisible by 3.

He has a huge number $s$. Polycarp wants to cut from it the maximum number of numbers that are divisible by $3$. To do this, he makes an arbitrary number of vertical cuts between pairs of adjacent digits. As a result, after $m$ such cuts, there will be $m+1$ parts in total. Polycarp analyzes each of the obtained numbers and finds the number of those that are divisible by $3$.

For example, if the original number is $s=3121$, then Polycarp can cut it into three parts with two cuts: $3|1|21$. As a result, he will get two numbers that are divisible by $3$.

Polycarp can make an arbitrary number of vertical cuts, where each cut is made between a pair of adjacent digits. The resulting numbers cannot contain extra leading zeroes (that is, the number can begin with 0 if and only if this number is exactly one character '0'). For example, 007, 01 and 00099 are not valid numbers, but 90, 0 and 10001 are valid.

What is the maximum number of numbers divisible by $3$ that Polycarp can obtain?
The first line of the input contains a positive integer $s$. The number of digits of the number $s$ is between $1$ and $2\cdot10^5$, inclusive. The first (leftmost) digit is not equal to 0.
3121
2
6
1
1000000000000000000000000000000000
33
201920181
4
4
0
10
1
11
0
12
1
13
1
31
1
14139582796
6
1670000
5
604500
5
40041
2
10000170
5
def div3(s, index_0, index_1):
    c = 0
    for i in range(index_0, index_1+1):
        c += int(s[i])
        c = c%3
    if c == 0:
        return True
    return False


s = input()
strings_list = [s]
d = 0
c = 0
while True:
    next_string_list = []
    for string in strings_list:
        i = 0
        keep = 0
        to_keep = []
        while i < len(string)-d:
            if div3(string, i, i+d):
                c += 1
                if i != keep:
                    to_keep.append((keep, i-1))
                i += d+1
                keep = i
            else:
                i += 1
        if keep != i:
            to_keep.append((keep, len(string)-1))

        for keeping in to_keep:
            next_string_list.append(string[keeping[0]:keeping[1]+1])
    strings_list = next_string_list[:]
    
    d += 1

    for string in strings_list:
        if len(string) > d:
            break
    else:
        break


print(c)

# Fri Oct 01 2021 22:56:12 GMT+0300 (Москва, стандартное время)
