Return the number of distinct non-empty substrings of text that can be written as the concatenation of some string with itself (i.e. it can be written as a + a where a is some string).
 
Example 1:
Input: text = "abcabcabc"
Output: 3
Explanation: The 3 substrings are "abcabc", "bcabca" and "cabcab".

Example 2:
Input: text = "leetcodeleetcode"
Output: 2
Explanation: The 2 substrings are "ee" and "leetcodeleetcode".

 
Constraints:

1 <= text.length <= 2000
text has only lowercase English letters.

```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 distinctEchoSubstrings(self, text: str) -> int:\n        \n        \n        s = set()\n        res = 0\n        for i in range(0, len(text), 1):\n            for j in range(i + 1, len(text), 2):\n                mid = (i + j - 1) // 2\n                t1 = text[i:mid+1]\n                t2 = text[mid+1:j+1]\n                # print(i, j, mid, t1, t2)\n                \n                if t1 == t2 and t1 not in s:\n                    s.add(text[i:mid+1])\n                    res += 1                \n                    \n        return len(s)\n        \n        \n        n=len(s)\n        dp=[0 for i in range(n)]\n        \n        dp[0]=ord(s[0])-ord('a')\n        \n        pw=[0]*(n+1)\n        \n        pw[0]=1\n        \n        curr=26\n        \n        for i in range(1,n):\n            dp[i]=dp[i-1]+curr*(ord(s[i])-ord('a'))\n            pw[i]=curr\n            curr=curr*26\n            \n        pw[-1]=curr\n        \n        #print(dp)\n        \n        st=set()\n        \n        for i in range(n):\n            for j in range(i+1,n,2):\n                \n                mid=(j+i)//2\n                \n                if i!=0:\n                    x1=dp[mid]-dp[i-1]\n                else:\n                    x1=dp[mid]\n                \n                x2=dp[j]-dp[mid]\n                \n                #print(x1,x2,s[i:mid+1],s[mid+1:j+1])\n                \n                if x2==x1*(pw[mid-i+1]):\n                    if s[i:mid+1]==s[mid+1:j+1]:\n                        st.add(s[i:j+1])\n                        #print(st)\n        return len(st) "
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'distinctEchoSubstrings'
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: 5776