Barney lives in NYC. NYC has infinite number of intersections numbered with positive integers starting from 1. There exists a bidirectional road between intersections i and 2i and another road between i and 2i + 1 for every positive integer i. You can clearly see that there exists a unique shortest path between any two intersections. [Image] 

Initially anyone can pass any road for free. But since SlapsGiving is ahead of us, there will q consecutive events happen soon. There are two types of events:

1. Government makes a new rule. A rule can be denoted by integers v, u and w. As the result of this action, the passing fee of all roads on the shortest path from u to v increases by w dollars. 

2. Barney starts moving from some intersection v and goes to intersection u where there's a girl he wants to cuddle (using his fake name Lorenzo Von Matterhorn). He always uses the shortest path (visiting minimum number of intersections or roads) between two intersections.

Government needs your calculations. For each time Barney goes to cuddle a girl, you need to tell the government how much money he should pay (sum of passing fee of all roads he passes).


-----Input-----

The first line of input contains a single integer q (1 ≤ q ≤ 1 000).

The next q lines contain the information about the events in chronological order. Each event is described in form 1 v u w if it's an event when government makes a new rule about increasing the passing fee of all roads on the shortest path from u to v by w dollars, or in form 2 v u if it's an event when Barnie goes to cuddle from the intersection v to the intersection u.

1 ≤ v, u ≤ 10^18, v ≠ u, 1 ≤ w ≤ 10^9 states for every description line.


-----Output-----

For each event of second type print the sum of passing fee of all roads Barney passes in this event, in one line. Print the answers in chronological order of corresponding events.


-----Example-----
Input
7
1 3 4 30
1 4 1 2
1 3 6 8
2 4 3
1 6 1 40
2 3 7
2 2 4

Output
94
0
32



-----Note-----

In the example testcase:

Here are the intersections used: [Image]   Intersections on the path are 3, 1, 2 and 4.  Intersections on the path are 4, 2 and 1.  Intersections on the path are only 3 and 6.  Intersections on the path are 4, 2, 1 and 3. Passing fee of roads on the path are 32, 32 and 30 in order. So answer equals to 32 + 32 + 30 = 94.  Intersections on the path are 6, 3 and 1.  Intersections on the path are 3 and 7. Passing fee of the road between them is 0.  Intersections on the path are 2 and 4. Passing fee of the road between them is 32 (increased by 30 in the first event and by 2 in the second).

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from functools import lru_cache\nfrom collections import defaultdict\nfrom itertools import tee\n\n\nprice = defaultdict(dict)\n\n\ndef add(start, end, w):\n    nonlocal price\n    for x, y in get_way(start, end):\n\n        if x not in price:\n            price[x] = defaultdict(lambda: 0)\n\n        if y not in price:\n            price[y] = defaultdict(lambda: 0)\n\n        price[x][y] += w\n        price[y][x] += w\n\n\ndef get_price(start, end):\n    result = 0\n    for x, y in get_way(start, end):\n        if x in price:\n            result += price[x][y]\n    return result\n\n\n@lru_cache(maxsize=1000)\ndef get_way(start, end):\n    def _get_raw_way():\n        nonlocal start, end\n        l_way, r_way = [start], [end]\n        while True:\n            l = l_way[-1] // 2\n            if l: l_way.append(l)\n            r = r_way[-1] // 2\n            if r: r_way.append(r)\n\n            if r_way[-1] == start:\n                return r_way\n            union = set(l_way) & set(r_way)\n            if union:\n                #print(l_way)\n                #print(r_way)\n                r_way = r_way[:r_way.index(max(union))]\n                l_way = l_way[:l_way.index(max(union))]\n                #print(l_way)\n                #print(r_way)\n                #print(r_way)\n                #del r_way[-1]\n                r_way.reverse()\n                return l_way + [union.pop()] + r_way\n\n    #print(_get_raw_way())\n    a, b = tee(_get_raw_way())\n    next(b, None)\n    return list(zip(a, b))\n\n#\nq = int(input())\nfor _ in range(q):\n    data = list(map(int, input().split(' ')))\n    if data[0] == 1:\n        add(data[1], data[2], data[3])\n    else:\n        print(get_price(data[1], data[2]))\n\n#print(get_way(568636620057521218, 935366325112217858))\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: