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)

rank = []
p = []
w = []

def makeSet(x):
    p.append(x)
    rank.append(0)
    w.append(0)


def union(x, y):
    link(findSet(x), findSet(y))


def link(x, y):
    if rank[x] > rank[y]:
        p[y] = x

    else:
        p[x] = y
        if rank[x] == rank[y]:
            rank[y] = rank[y] + 1


def findSet(x):
    if p[x] == x:
        return x

    i = findSet(p[x])
    w[x] += w[p[x]]
    p[x] = i
    return i


def same(x, y):
    return findSet(x) == findSet(y)

def relate (x,y,z):
    i = findSet(x)
    j = findSet(y)

    if rank[i] < rank[j]:
        p[i] = j
        w[i] = z - w[x] + w[y]
    else:
        p[j] = i
        w[j] = -z - w[y] + w[x]
        if rank[i] == rank[j]:
            rank[i] += 1

n, q = map(int, input().split())
for i in range(n):
    makeSet(i)
for i in range(q):
    com, *cmd = map(int, input().split())
    if com == 0:
        relate(cmd[0], cmd[1],cmd[2])
    else:
        x, y = cmd
        if same(x, y):
            print(w[x] - w[y])
        else:
            print("?")