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 WeightedUnionFind():
    def __init__(self,n):
        self.n=n
        self.parents=[-1]*n
        self.differ=[0]*n

    def find(self,x):
        if self.parents[x]<0:
            return x
        else:
            r=self.find(self.parents[x])
            self.differ[x]+=self.differ[self.parents[x]]
            self.parents[x]=r
            return self.parents[x]

    def unite(self,x,y,w):
        xp=self.find(x)
        yp=self.find(y)
        w=w+self.differ[x]-self.differ[y]

        if xp!=yp:
            if self.parents[xp]>self.parents[yp]:
                xp,yp=yp,xp
                w=-w

            self.parents[xp]+=self.parents[yp]
            self.parents[yp]=xp
            self.differ[yp]=w

    def diff(self,x,y):
        xp=self.find(x)
        yp=self.find(y)
        if xp==yp:
            return True,self.differ[y]-self.differ[x]
        else:
            return False,0

n,q=map(int,input().split())
WUF=WeightedUnionFind(n)
for i in range(q):
    query=list(map(int,input().split()))
    if query[0]==0:
        WUF.unite(query[1],query[2],query[3])
    elif query[0]==1:
        judge,diff=WUF.diff(query[1],query[2])
        if judge:
            print(diff)
        else:
            print("?")