human
Can you provide a Python program to find the smallest DPC of a given string, or return `-1` if there is no such given the following:
Solve in Python:
# Task
 You are given a string consisting of `"D", "P" and "C"`. A positive integer N is called DPC of this string if it satisfies the following properties: 
 
 ```
 For each i = 1, 2, ... , size of the string:

 If i-th character is "D", then N can be divided by i
 If i-th character is "P", then N and i should be relatively prime
 If i-th character is "C", then N should neither be divided by i 
                           nor be relatively prime with i```

Your task is to find the smallest DPC of a given string, or return `-1` if there is no such. The result is guaranteed to be `<= 10^9`.

# Example
 For `s = "DDPDD"`, the result should be `20`.
 
 `"DDPDD"` means `N` should `divided by 1,2,4,5`, and `N,3` should be relatively prime. The smallest N should be `20`.

# Input/Output

 - `[input]` string `s`

  The given string

 - `[output]` an integer

  The smallest DPC of `s` or `-1` if it doesn't exist.
assistant
#Here is Python program to find the smallest DPC of a given string, or return `-1` if there is no such.

from fractions import gcd

def DPC_sequence(s):
    res = 1
    
    for i, c in enumerate(s, 1):
        if c == 'D':
            res *= i // gcd(i, res)
            
    def check_DPC_at(i, c):
        if c == 'D':
            return gcd(i, res) == i
        elif c == 'C':
            return gcd(i, res) in range(2, i)
        elif c == 'P':
            return gcd(i, res) == 1
            
    return res if all(check_DPC_at(*e) for e in enumerate(s, 1)) else -1