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
from collections import *
from heapq import *
from bisect import *
from itertools import *
from functools import *
from math import *
from string import *
import sys

input = sys.stdin.readline


def solve():
    s = input().strip()
    n = len(s)

    def neighbors(i):
        for j in range(i, n):
            sz = j - i + 1
            val = int(s[i : j + 1])

            if sz > 1 and s[i] + s[i + 1] == "00":
                continue

            weight = val % 3 == 0
            yield weight, j + 1

    @cache
    def dp(i):
        if i == n:
            return 0

        ans = 0
        for weight, nei in neighbors(i):
            ans = max(ans, weight + dp(nei))
        return ans

    print(dp(0))


def main():
    tests = 1
    for _ in range(tests):
        solve()


if __name__ == "__main__":
    main()
