# Task
 A range-collapse representation of an array of integers looks like this: `"1,3-6,8"`, where `3-6` denotes the range from `3-6`, i.e. `[3,4,5,6]`. 
 
 Hence `"1,3-6,8"` = `[1,3,4,5,6,8]`. Some other range-collapse representations of `[1,3,4,5,6,8]` include `"1,3-5,6,8", "1,3,4,5,6,8", etc`.

 Each range is written in the following format `"a-b"`, where `a < b`, and the whole range must belong to the array in an increasing order.

 You are given an array `arr`. Your task is to find the number of different range-collapse representations of the given array.

# Example
 
 For `arr = [1,3,4,5,6,8]`, the result should be `8`.
 ```
 "1,3-4,5,6,8"
 "1,3-4,5-6,8"
 "1,3-5,6,8"
 "1,3-6,8"
 "1,3,4-5,6,8"
 "1,3,4-6,8"
 "1,3,4,5-6,8"
 "1,3,4,5,6,8"```

# Input/OutPut


 - `[input]` integer array `arr`

  sorted array of different positive integers.


 - `[output]` an integer

  the number of different range-collapse representations of the given array.

```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 = '\ndef pair_apply(a, fn): \n    """\n    Apply a funtion to each pair of consecutive \n    values in the array and return the resultant array\n    """\n    return [fn(x, y) for x, y in zip(a, a[1:])]\n\ndef run_length_encode(a):\n    """Run length encode the given array"""\n    a = [(x, 1) for x in a]\n    i = 0\n    while i < len(a) - 1:\n        if a[i][0] == a[i + 1][0]:\n            a[i] = (a[i][0], a[i][1] + 1)\n            del a[i + 1]\n        else:\n            i += 1\n    return a\n\ndef descriptions(arr):\n    """\n    Caluculate number of possible range collapse \n    permutations for givven array\n    """\n    deltas = pair_apply(arr, lambda x, y: y - x)\n    rle_deltas = run_length_encode(deltas)\n    result = 1\n    for delta, count in rle_deltas:\n        if delta == 1:\n            result *= 2 ** count\n    return result\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'descriptions'
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: 6288