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 CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
using namespace std;

const int NIL = -1;
const int MAX = 1 << 21;

struct Node {
	int node, weight, parent;
};

Node forests[100010];
int height[100010];

int findSet(int x) {
	vector<int>tree;
	int sum, i;
	while (forests[x].parent != forests[x].node) {
		tree.push_back(x);
		x = forests[x].parent;
	}
	for (vector<int>::iterator it = tree.begin(); it != tree.end(); it++) {
		sum = 0;
		i = *it;
		while (forests[i].parent != i) {
			sum += forests[i].weight;
			i = forests[i].parent;
		}
		forests[*it].parent = x;
		forests[*it].weight = sum;
	}
	return x;
}

void unite(int x, int y, int z)
{
	int X, Y;
	X = findSet(x);
	Y = findSet(y);
	if (height[X] > height[Y]) {
		forests[Y].parent = X;
		forests[Y].weight = -forests[y].weight + forests[x].weight + z;
	}
	else if (height[X] < height[Y]) {
		forests[X].parent = Y;
		forests[X].weight = -forests[x].weight + forests[y].weight - z;
	}
	else {
		forests[Y].parent = X;
		forests[Y].weight = -forests[y].weight + forests[x].weight + z;
		height[X]++;
	}
}

int main(void)
{
	int n, q, com, x, y, z, X, Y;
	cin >> n >> q;
	for (int i = 0; i < n; i++) {
		forests[i].node = i;
		forests[i].weight = 0;
		forests[i].parent = i;
	}
	for (int i = 0; i < q; i++) {
		cin >> com;
		if (com) {
			cin >> x >> y;
			X = findSet(x);
			Y = findSet(y);
			if (X == Y)
				cout << forests[y].weight - forests[x].weight << endl;
			else
				cout << "?" << endl;
		}
		else {
			cin >> x >> y >> z;
			X = findSet(x);
			Y = findSet(y);
			if (X == Y)
				continue;
			else
				unite(x, y, z);
		}
	}
	return 0;
}