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:
import math

class weightedUnionTree:
    def __init__(self,n):
        self.par = [i for i in range(n+1)]
        self.rank = [0] * (n+1)
        self.weight = [0] * (n+1)

    def find(self,x):
        if self.par[x] == x:
            return x
        else:
            y = self.find(self.par[x])
            self.weight[x] += self.weight[self.par[x]]
            self.par[x] = y
            return y

    def union(self,x, y, w):
        rx = self.find(x)
        ry = self.find(y)
        #self.isThere[x] = True; self.isThere[y] = True

        if self.rank[rx] < self.rank[ry]:
            self.par[rx] = ry
            self.weight[rx] = w - self.weight[x] + self.weight[y]

        else:
            self.par[ry] = rx
            self.weight[ry] = -w - self.weight[y] + self.weight[x]

            if self.rank[rx] == self.rank[ry]:
                self.rank[rx] += 1

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

    def diff(self, x, y):
        """
        print("diff: ",end="")
        print(self.weight[x],end=" ")
        print(self.weight[y],end=" ")
        #print(self.isThere)
        """

        if(self.same(x, y)): #conditional branch
            print(self.weight[x] - self.weight[y])
        else:
            print("?")


if __name__ == "__main__":
    n, q = (int(p) for p in input().split())
    tree = weightedUnionTree(n)
    #for i in range(n):
    #    queue.append(0)
    for i in range(q):
        question, num = input().split(' ', 1)
        #print(question)
        #print(input)
        if(int(question) == 0):
            #print("relate")
            x, y, z = num.split(' ')
            tree.union(int(x), int(y), int(z))
        else:
            #print("diff")
            x, y = num.split(' ')
            tree.diff(int(x), int(y))