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 defaultdict

n = list(map(int, input()))
le = len(n)
memo = defaultdict(int)

def dp(index, flag, summ):
    if (index, flag) in memo:
        return memo[(index, flag)]

    if index >= le:
        return 0

    max_parts = 0
    if flag:
        max_parts = max(max_parts, dp(index + 1, False, 0) + (1 if summ % 3 == 0 and summ > 0 else 0))
    
    max_parts = max(max_parts, dp(index + 1, True, summ + n[index]))

    memo[(index, flag)] = max_parts
    return max_parts

print(dp(0, False, 0))
