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
num = input()
length = len(num)
res = -float('inf')

def compute(num, pointer, count):
    global res

    if pointer >= length:
        res = max(res, count)
        return 

    temp = num[:pointer + 1]
    
    if res > count + (len(num) - pointer):
        return 

    elif not temp:
        res = max(res, count)
        return 

    elif len(temp) > 1 and temp[0] == "0":
        return 

    elif int(temp) % 3 == 0:
        compute(num[pointer + 1:], 0, count + 1)

    else:
        compute(num[pointer + 1:], 0, count)

    compute(num, pointer + 1, count)

compute(num, 0, 0)
print(res)