Problem:
Weighted Union Find Trees

There is a sequence $A = a_0, a_1, ..., a_{n-1}$. You are given the following information and questions.

relate$(x, y, z)$: $a_y$ is greater than $a_x$ by $z$

diff$(x, y)$: report the difference between $a_x$ and $a_y$ $(a_y - a_x)$

Input

$n \; q$
$query_1$
$query_2$
:
$query_q$

In the first line, $n$ and $q$ are given. Then, $q$ information/questions are given in the following format.

0 $x \; y\; z$

or

1 $x \; y$

where '0' of the first digit denotes the relate information and '1' denotes the diff question.

Output

For each diff question, print the difference between $a_x$ and $a_y$ $(a_y - a_x)$.

Constraints

$2 \leq n \leq 100,000$

$1 \leq q \leq 200,000$

$0 \leq x, y < n$

$x \ne y$

$0 \leq z \leq 10000$

There are no inconsistency in the given information

Sample Input

5 6
0 0 2 5
0 1 2 3
1 0 1
1 1 3
0 1 4 8
1 0 4

Sample Output

2
?
10

Solution in Python3 (judge verdict: Accepted)

import sys
sys.setrecursionlimit(50000)

def findset(x,element,weight):
    if(x != element[x]):
        element[x],s = findset(element[x],element,weight)
        weight[x] += s
    return element[x],weight[x]

def union(x,y,element,weight,w):
    x,wx = findset(x,element,weight)
    y,wy = findset(y,element,weight)
    link(x,y,w+wy-wx,element,weight)

def link(x,y,z,element,weight):

    element[x] = y
    weight[x] = z

n,q = map(int, input().split());

element = [i for i in range(n)]
weight = [0 for i in range(n)]

for i in range(q):
    inp = map(int, input().split());
    inp = list(inp)    
    if(inp[0] == 0):
        x,y,w = inp[1],inp[2],inp[3]
        union(x,y,element,weight,w)
    else:
        x,y = inp[1],inp[2]
        x,wx = findset(x,element,weight)
        y,wy = findset(y,element,weight)
        if(x == y):
            print(wx-wy)
        else:
            print('?')