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 UnionFind():

    def __init__(self, s):
        self.nodes = [-1 for _ in range(s)]
        self.rank = [0 for _ in range(s)]
        self.weight = [0 for _ in range(s)]

    def find(self, x):
        if self.nodes[x] < 0:
            return x
        else:
            root = self.find(self.nodes[x])
            self.weight[x] += self.weight[self.nodes[x]]
            self.nodes[x] = root
            return root

    def union(self, x, y, z):
        s_1 = self.find(x)
        s_2 = self.find(y)
        if s_1 == s_2:
            return False
        if self.rank[s_1] < self.rank[s_2]:
            self.nodes[s_1] = s_2
            self.weight[s_1] = z - self.weight[x] + self.weight[y]
        elif self.rank[s_1] > self.rank[s_2]:
            self.nodes[s_2] = s_1
            self.weight[s_2] = self.weight[x] - self.weight[y] - z
        else:
            self.nodes[s_2] = s_1
            self.weight[s_2] = self.weight[x] - self.weight[y] - z
            self.rank[s_1] += 1
        return True

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

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


if __name__ == "__main__":
    n, q = map(int, input().split())
    sets = UnionFind(n)
    for i in range(q):
        inputs = [int(i) for i in input().split()]
        if inputs[0] == 0:
            sets.union(inputs[1], inputs[2], inputs[3])
        else:
            if sets.is_same(inputs[1], inputs[2]):
                print(sets.diff(inputs[1], inputs[2]))
            else:
                print("?")