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 <bits/stdc++.h>
using namespace std;

template <typename T>
class weighted_quick_find {
	vector<pair<int, T>> data;
	vector<vector<int>> all;
public:
	weighted_quick_find(int n) : data(n), all(n, vector<int>(1)) {
		for (int i = 0; i < n; i++) {
			data[i].first = i;
			all[i][0] = i;
		}
	}
	void unite(int a, int b, T d) {
		if (same(a, b)) return;
		d += data[a].second - data[b].second;
		a = data[a].first;
		b = data[b].first;
		if (all[a].size() < all[b].size()) swap(a, b), d = -d;
		for (auto& id : all[b]) {
			data[id] = { a, data[id].second + d };
		}
		copy(all[b].begin(), all[b].end(), back_inserter(all[a]));
	}
	bool same(int a, int b) const {
		return data[a].first == data[b].first;
	}
	T dist(int a, int b) const {
		return data[b].second - data[a].second;
	}
};

int main()
{
	ios::sync_with_stdio(false), cin.tie(0);
	int n, q;
	cin >> n >> q;
	weighted_quick_find<int> wqf(n);
	while (q--) {
		int com, x, y;
		cin >> com >> x >> y;
		if (com == 0) {
			int z;
			cin >> z;
			wqf.unite(x, y, z);
		}
		else if (wqf.same(x, y)) {
			printf("%d\n", wqf.dist(x, y));
		}
		else {
			puts("?");
		}
	}
	return 0;
}