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 P_UnionFind:
    def __init__(self, n):
        self.p=[i for i in range(n)]
        self.r=[0 for i in range(n)]
        self.d=[0 for i in range(n)]
    def root(self,x):
        if self.p[x]==x:
            return x
        else:
            tmp = self.root(self.p[x])
            self.d[x] += self.d[self.p[x]]
            self.p[x] = tmp
            return self.p[x]
    
    def weight(self,x):
        self.root(x)
        return self.d[x]

    def diff(self,x,y):
        if self.root(x)==self.root(y):
            return self.weight(y)-self.weight(x)
        else:
            return '?'

    def uni(self,x,y,w):
        w+=self.weight(x)
        w-=self.weight(y)
        x=self.root(x)
        y=self.root(y)
        if(x==y):
            return
        if self.r[x]<self.r[y]:
            self.p[x]=y
            self.d[x]=-w
        else:
            self.p[y]=x
            self.d[y]=w
            if self.r[x]==self.r[y]:
                self.r[x]+=1
    
    def same(self,x,y):
        return self.root(x)==self.root(y)

n,q=map(int,input().split())
uf=P_UnionFind(n)
ans=[]
for i in range(q):
    d=list(map(int,input().split()))
    if d[0]==0:
        c,x,y,z=d
        uf.uni(x,y,z)
    else:
        c,x,y=d
        ans.append(uf.diff(x,y))
print(*ans,sep='\n')