Problem: 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 $a_y$ $(a_y - a_x)$

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

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 $a_y$ $(a_y - a_x)$.

Example

Input

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


Output

2
?
10

Solution (in PYTHON3):

Solution:
class WeightedUnionFindTree:

    def __init__(self, n_nodes):
        super().__init__()
        self.par = [i for i in range(n_nodes)]
        self.rank = [0] * n_nodes
        self.weights = [0] * n_nodes

    def find(self, x):
        if self.par[x] == x:
            return x
        root = self.find(self.par[x])
        self.weights[x] += self.weights[self.par[x]]
        self.par[x] = root
        return root

    def unite(self, x, y, weight=0):
        root_x, root_y = self.find(x), self.find(y)
        if root_x == root_y:
            return
        if self.rank[root_x] < self.rank[root_y]:
            self.par[root_x] = root_y
            self.weights[root_x] = weight - self.weights[x] + self.weights[y]
        else:
            self.par[root_y] = root_x
            self.weights[root_y] = - \
                (weight - self.weights[x] + self.weights[y])
            if self.rank[root_x] == self.rank[root_y]:
                self.rank[root_x] += 1

    def is_same(self, x, y):
        return self.find(x) == self.find(y)

    def diff(self, x, y):
        return self.weights[x] - self.weights[y]


if __name__ == "__main__":
    N, Q = map(int, input().split())
    uft = WeightedUnionFindTree(N)
    ans = []
    for _ in range(Q):
        type_, u, v, *weight = map(int, input().split())
        if type_ == 0:
            uft.unite(u, v, weight[0])
        else:
            ans.append(uft.diff(u, v) if uft.is_same(u, v) else '?')
    for a in ans:
        print(a)