Lorenzo Von Matterhorn

有一棵由无数个编号从 $1$ 开始的节点组成的树，$i$ 与 $2\times i$ 和 $2\times i+1$ 之间有一条无向边，任意两点间有唯一最短路。 最初，所有的边权为 $0$。有 $q$ 次操作如下： 1. `1 v u w` 表示将 $u$ 到 $v$ 最短路径中的所有边边权加上 $w$。 2. `2 v u` 表示询问从 $u$ 到 $v$ 最短路径上的边权之和。 对于每个操作 $2$，输出答案。 $\text{p.s}$：这里的最短路径指到达最少数量的点或边的路径。

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. 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).

The first line of input contains a single integer $ q $ ( $ 1<=q<=1000 $ ). 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.

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.

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

94
0
32

In the example testcase: Here are the intersections used: 1. Intersections on the path are $ 3 $ , $ 1 $ , $ 2 $ and $ 4 $ . 2. Intersections on the path are $ 4 $ , $ 2 $ and $ 1 $ . 3. Intersections on the path are only $ 3 $ and $ 6 $ . 4. 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 $ . 5. Intersections on the path are $ 6 $ , $ 3 $ and $ 1 $ . 6. Intersections on the path are $ 3 $ and $ 7 $ . Passing fee of the road between them is $ 0 $ . 7. 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).