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>

struct Node {
	int parent;
	int dif_to_parent;
};

int root(Node* nodes, int x)
{
	if (nodes[x].parent == x) return x;
	else return root(nodes, nodes[x].parent);
}

bool isSame(Node* nodes, int x, int y)
{
	return root(nodes, x) == root(nodes, y);
}

void unite(Node* nodes, int x, int y, int dif)
{
	int x_depth = 0;
	int y_depth = 0;
	while (nodes[x].parent != x) {
		x_depth += nodes[x].dif_to_parent;
		x = nodes[x].parent;
	}
	while (nodes[y].parent != y) {
		y_depth += nodes[y].dif_to_parent;
		y = nodes[y].parent;
	}
	if (x_depth + dif > y_depth) {
		nodes[y].parent = x;
		nodes[y].dif_to_parent = x_depth + dif - y_depth;
	} else {
		nodes[x].parent = y;
		nodes[x].dif_to_parent = y_depth - x_depth - dif;
	}
}

int difference(Node* nodes, int x, int y)
{
	int x_depth = 0;
	int y_depth = 0;
	int rx = x;
	int ry = y;
	while (nodes[rx].parent != rx) {
		x_depth += nodes[rx].dif_to_parent;
		rx = nodes[rx].parent;
	}
	while (nodes[ry].parent != ry) {
		y_depth += nodes[ry].dif_to_parent;
		ry = nodes[ry].parent;
	}
	nodes[x].parent = rx;
	nodes[x].dif_to_parent = x_depth;
	nodes[y].parent = ry;
	nodes[y].dif_to_parent = y_depth;
	return y_depth - x_depth;
}

int main()
{	
	int n, q; std::cin >> n >> q;
	
	Node* nodes = new Node[n];
	for (int i=0; i<n; i++) {
		nodes[i].parent = i;
	}
	
	for (int i=0; i<q; i++) {
		int op, x, y, z;
		std::cin >> op;
		if (op==0) {
			std::cin >> x >> y >> z;
			unite(nodes, x, y, z);
		} else {
			std::cin >> x >> y;
			if (isSame(nodes, x, y)) std::cout << difference(nodes, x, y) << std::endl;
			else std::cout << "?" << std::endl;
		}
	}
	
	delete[] nodes;
	
	return 0;
}