Given an integer array A, and an integer target, return the number of tuples i, j, k  such that i < j < k and A[i] + A[j] + A[k] == target.
As the answer can be very large, return it modulo 109 + 7.
 
Example 1:
Input: A = [1,1,2,2,3,3,4,4,5,5], target = 8
Output: 20
Explanation: 
Enumerating by the values (A[i], A[j], A[k]):
(1, 2, 5) occurs 8 times;
(1, 3, 4) occurs 8 times;
(2, 2, 4) occurs 2 times;
(2, 3, 3) occurs 2 times.

Example 2:
Input: A = [1,1,2,2,2,2], target = 5
Output: 12
Explanation: 
A[i] = 1, A[j] = A[k] = 2 occurs 12 times:
We choose one 1 from [1,1] in 2 ways,
and two 2s from [2,2,2,2] in 6 ways.

 
Constraints:

3 <= A.length <= 3000
0 <= A[i] <= 100
0 <= target <= 300

```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 threeSumMulti(self, A: List[int], target: int) -> int:\n        ADict = {}\n        A = sorted(A)\n        print(A)\n        for a in A:\n            if a in ADict:\n                ADict[a]+=1\n            else:\n                ADict[a] = 1\n        ijSame = False\n        keys = sorted(ADict)\n        totWays = 0\n        # check all same:\n        for i in range(len(keys)):\n            if keys[i] > target:\n                 break\n            elif ADict[keys[i]]<3:\n                continue\n            elif keys[i]*3 == target:\n                numOcc = ADict[keys[i]]\n                totWays += numOcc*(numOcc-1)*(numOcc-2)/6\n        \n        if len(keys)==1:\n            return int(totWays%(10**9 + 7))\n        # 2 are same:\n        for i in range(len(keys)):\n            if keys[i] > target:\n                 break\n            elif ADict[keys[i]]<2:\n                continue\n            else:\n                sum = keys[i]*2\n                remain = target - sum\n                if (not(remain==keys[i]) and remain in keys):\n                    numDoubleOcc = ADict[keys[i]]\n                    numSingleOcc = ADict[remain]\n                    totWays += numDoubleOcc*(numDoubleOcc-1)/2*numSingleOcc\n        if len(keys)==2:\n            return int(totWays%(10**9 + 7))\n        # all distinct\n        for i in range(len(keys)):\n            if keys[i] > target:\n                 break\n            for j in range(i+1, len(keys)):\n                sum = keys[i] + keys[j]\n                if sum > target:\n                    break\n                remaining = target - sum\n                if remaining in keys[j+1:]:\n                    totWays += ADict[keys[i]] *ADict[keys[j]] *ADict[remaining]\n                \n        return int(totWays%(10**9 + 7))\n        \n        \n#         for i in range(len(keys)):\n#             if keys[i] > target:\n#                  return totWays\n                \n#             if ADict[keys[i]] ==1:\n#                 startJ = i+1\n#             else:\n#                 startJ = i\n#                 ijSame = True\n#             for j in range(startJ, len(keys)):\n#                 sum = keys[i] + keys[j]\n#                 if sum > target:\n#                      break\n#                 remaining = target - sum\n#                 if remaining in keys:\n#                      totWays+=1\n#         #             tempA.remove(remaining)\n                \n            \n        #for ele in ADict.keys():\n            \n        \n        \n        # A = sorted(A)\n        # #print(A)\n        # if len(A)<3:\n        #     return 0\n        # totWays = 0\n        # for i in range (len(A)):\n        #     if A[i] >target:\n        #         return totWays\n        #     for j in range (i+1, len(A)):\n        #         tempA = A[j+1:].copy()\n        #         sum = A[i] + A[j]\n        #         if sum > target:\n        #             break\n        #         remaining = target - sum\n        #         while remaining in tempA:\n        #             totWays+=1\n        #             tempA.remove(remaining)\n        #             #print (str(A[i]) + \\" \\" + str(A[j]) + \\" \\" + str(remaining))\n        # return totWays\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'threeSumMulti'
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: 7165