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
input = sys.stdin.readline

class WeightedUnionFind:
    def __init__(self, N):
        self.parent = list(range(N))
        self.rank = [0] * N
        self.weight = [0] * N

    def find(self, x):
        stack = [x]
        while self.parent[x] != x:
            x = self.parent[x]
            stack.append(x)
        r = stack[-1]
        while stack:
            x = stack.pop()
            self.weight[x] += self.weight[self.parent[x]]
            self.parent[x] = r
        return r

    def unite(self, x, y, w):
        rx = self.find(x)
        ry = self.find(y)
        w += self.weight[x] - self.weight[y]
        x = rx
        y = ry
        if x == y:
            return False

        if self.rank[x] < self.rank[y]:
            x, y = y, x
            w = -w
        if self.rank[x] == self.rank[y]:
            self.rank[x] += 1
        self.parent[y] = x
        self.weight[y] = w
        return True

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

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

n, q = map(int, input().split())
wuf = WeightedUnionFind(n)
for _ in range(q):
    t, *data = map(int, input().split())
    if t == 0:
        x, y, z = data
        wuf.unite(x, y, z)
    else:
        x, y = data
        if not wuf.same(x, y):
            print('?')
        else:
            print(wuf.diff(x, y))