Given a string S, count the number of distinct, non-empty subsequences of S .
Since the result may be large, return the answer modulo 10^9 + 7.
 
Example 1:
Input: "abc"
Output: 7
Explanation: The 7 distinct subsequences are "a", "b", "c", "ab", "ac", "bc", and "abc".


Example 2:
Input: "aba"
Output: 6
Explanation: The 6 distinct subsequences are "a", "b", "ab", "ba", "aa" and "aba".


Example 3:
Input: "aaa"
Output: 3
Explanation: The 3 distinct subsequences are "a", "aa" and "aaa".



 
 
Note:

S contains only lowercase letters.
1 <= S.length <= 2000

```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 = 'class Solution:\n    def distinctSubseqII(self, S: str) -> int:\n        def itertools_appr():\n            if not S: return 0\n            from itertools import combinations\n            n = len(S)\n            MOD = 1000_000_000 + 7\n            l = 0\n            for i in range(1,n+1):\n                l += len(set(combinations(S, i))) % MOD\n            return l\n        \n        def from_soln():\n            \'\'\'\n            Imagine we knew the subsequence count without the last char, dp[-1]\n            dp[-1] should be twice of the previous one. However we need to account\n            for the presence of the same last char previously.\n            S = \\"abab\\"\n            dp[0], with chars upto S[0] = { \'\', \'a\' }\n            dp[1], with chars upto S[1] = dp[1] * 2 - subseqs we would have\n                double counted. {\'\', \'a\', \'b\', \'ab\'}\n                = 4\n            dp[2], with chars upto S[2] = 2*dp[1] - adj for double counting\n                {\'\', \'a\', \'b\', \'ab\'} --> dp[1]\n                {\'a\', \'aa\', \'ba\', \'aba\'} --> dp[1] + \'a\'\n                \'a\' is double counted = dp[last[\'a\']] - 1\n                = 7\n            dp[3], with chars upto S[3] = 2*dp[2] - adjustments for double counting\n                {\'\',\'a\',\'b\',\'ab\',\'aa\',\'ba\',\'aba\'} <-- dp[2]\n                {\'b\',\'ab\',\'bb\',\'abb\',\'aab\',\'bab\',\'abab\'} <-- dp[2] + \'b\'\n                \'b\', \'ab\' are double counted = dp[last[\'b\']] - 1\n                = 14\n            \n            dp[k] = 2*dp[k-1] - dp[last[S[k]]] - 1, (1 for \'\')\n            \'\'\'\n            dp = [1]\n            last = {}\n            for i,x in enumerate(S):\n                dp.append(2*dp[-1])\n                if x in last:\n                    dp[-1] -= dp[last[x]]\n                last[x] = i\n            return (dp[-1] - 1) % (10**9+7)\n        return from_soln()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'distinctSubseqII'
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: 5994