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 sys

class WeightedUnionFind:
    def __init__(self, N:int):
        """N: 大きさ
        size: 連結成分の大きさ
        weight: rootからの重み
        """
        self.par = [i for i in range(N)]
        #self.size = [1]*N
        self.rank = [0]*N
        self.weight = [0]*N

    def root(self, x:int)->int:
        """根を求める"""
        if self.par[x] == x: # if root
            return x
        else:
            root_x = self.root(self.par[x]) # 経路圧縮
            self.weight[x] += self.weight[self.par[x]]
            self.par[x] = root_x
            return root_x

    def get_weight(self, x: int)->int:
        """x の重みを取得"""
        self.root(x) # 経路圧縮
        return self.weight[x]

    def get_diff(self, x:int, y:int)->int:
        """x と y の差分を取得"""
        if not self.is_same(x, y): return "?" # 判定不可
        return self.get_weight(y) - self.get_weight(x)

    def is_same(self, x:int, y:int)->bool:
        """x と y が同じ集合に属するか否か"""
        return self.root(x)==self.root(y)

    def unite(self, x:int, y:int, w:int)->bool:
        """weight[y] = weight[x]+w となるようにmerge(x が y の親)
        return True if merge 可能"""
        if self.is_same(x, y): return False
        root_x = self.root(x)
        root_y = self.root(y)
        w += (self.weight[x] - self.weight[y])
        if self.rank[root_x] < self.rank[root_y]:
            self.par[root_x] = root_y
            self.weight[root_x] = -w
        else:
            self.par[root_y] = root_x
            self.weight[root_y] = w
            if self.rank[root_x] == self.rank[root_y]:
                self.rank[root_x] += 1
        return True

    def get_size(self, x:int)->int:
        """xの属するグループのサイズ"""
        return self.size[self.root(x)]

if __name__ == "__main__":
    N,Q = map(int, sys.stdin.readline().split())
    UNITE,DIFF = 0,1
    wuf = WeightedUnionFind(N)
    for _ in range(Q):
        com,*x = map(int, sys.stdin.readline().split())
        if com==UNITE:
            wuf.unite(*x)
        else: # same
            print(wuf.get_diff(*x))