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 = [i for i in range(n)]
        self.rank = [0 for _ in range(n)]
        self.weight = [0 for _ in range(n)]
    def find(self,x):
        root = x
        stack = [root]
        while self.parents[root] != root:
            root = self.parents[root]
            stack.append(root)
        while stack:
            s = stack.pop()
            self.weight[s] += self.weight[self.parents[s]]
        while self.parents[x] != root:
            parent = self.parents[x]
            self.parents[x] = root
            x = parent
        return root
    def unite(self,x,y,w):
        xroot = self.find(x)
        yroot = self.find(y)
        if xroot == yroot:
            return
        xrank = self.rank[xroot]
        yrank = self.rank[yroot]
        if xrank < yrank:
            self.parents[xroot] = yroot
            self.weight[xroot] = w-self.weight[x]+self.weight[y]
        else:
            self.parents[yroot] = xroot
            self.weight[yroot] = -w+self.weight[x]-self.weight[y]
            if xrank == yrank:
                self.rank[xroot] += 1

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

N,Q = map(int,input().split())
uf = WeightedUnionFind(N)
ans = []

for _ in range(Q):
    q = list(map(int,input().split()))
    if q[0] == 0:
        uf.unite(q[1],q[2],q[3])
    else:
        if uf.find(q[1]) == uf.find(q[2]):
            ans.append(uf.diff(q[1],q[2]))
        else:
            ans.append('?')

print('\n'.join(map(str,ans)))