# 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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from math import gcd\n\ntry:\n    from math import prod\nexcept ImportError:\n    def prod(l, p=1):\n        for n in l: p *= n\n        return p\n\nmax_n = 1000000000\n\ndef DPC_sequence(s):\n    if s[0] == 'C':\n        return -1\n    primes = list(find_primes(len(s)))\n    pf = []\n    for p in primes:\n        if s[p-1] == 'C':\n            return -1\n        if s[p-1] == 'D':\n            pf.append(p)\n    #print(pf)\n    for p in pf:\n        for i in range(2*p-1, len(s), p):\n            if s[i] == 'P':\n                return -1\n    base = prod(pf)\n    nmax = min(prod(primes), max_n)\n    #print(base, nmax)\n    for n in range(base, nmax, base):\n        if test(s, n):\n            return n\n    return -1\n\ndef test(s, n):\n    for k in range(2, len(s)+1):\n        c = s[k-1]\n        if c == 'D':\n            if n % k != 0: return False\n        else:\n            if (gcd(n, k) == 1) != (c == 'P'): return False\n    return True\n\ndef find_primes(n):\n    if n < 2: return\n    yield 2\n    s = list(range(1, n+1, 2))\n    mroot = int(n ** 0.5)\n    half = (n+1) // 2\n    i = 1\n    m = 3\n    while m <= mroot:\n        if s[i]:\n            yield s[i]\n            j = m*m // 2\n            while j < half:\n                s[j] = 0\n                j += m\n        i += 1\n        m += 2\n    for x in s[i:]:\n        if x:\n            yield x\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'DPC_sequence'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6468