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
n = list(map(int, list(input())))
ans = 0
N = []
fl = 0
for i in range(len(n)):
    if n[i] == 0:
        N.append(n[fl:i])
        fl = i + 1
        ans += 1

if fl < len(n):
    N.append(n[fl:])

for n in N:
    # print(n)
    use = [False] * len(n)
    rui = [0]
    for i in range(1, 6):
        for j in range(0, len(n) - i + 1):
            # print(n[j:j+i])
            if not any(use[j:j+i]):
                if sum(n[j:j+i]) % 3 == 0:
                    ans += 1
                    for s in range(j, j + i):
                        use[s] = True

print(ans)
