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;

class WeightedUnionFind{
public:
	vector<int> Parent;
	vector<int> Rank;
	vector<long long> Weight;
	WeightedUnionFind(int n){
		++n;
		Parent.resize(n, 0);
		Rank.resize(n, 0);
		Weight.resize(n, 0);
		for(int i=0; i<n; ++i)
			Parent[i] = i;
	}

	int find(int x){
		if(Parent[x] == x) return x;
		int pastparent = Parent[x];
		Parent[x] = find(Parent[x]);
		Weight[x] += Weight[pastparent];
		return Parent[x];
	}

	bool unite(int x, int y, long long z){ // a[y] - a[x] == z
		int sx = x, sy = y;
		x = find(x);
		y = find(y);
		if(x == y) return false;
		if(Rank[x] < Rank[y]){
			Parent[x] = y;
			Weight[x] = z + Weight[sy] - Weight[sx];
		}else{
			Parent[y] = x;
			Weight[y] = - z - Weight[sy] + Weight[sx];
			if(Rank[x] == Rank[y]) ++Rank[x];
		}
		return true;
	}

	bool same(int x, int y){
		return find(x) == find(y);
	}

	long long cost(int x, int y){ // call only if same(x, y) == true
		return Weight[x] - Weight[y];
	}
};

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n, q;
	cin >> n >> q;
	WeightedUnionFind wuf(n);
	for(int i=0; i<q; ++i){
		int t;
		cin >> t;
		if(t == 0){
			int x, y;
			long long z;
			cin >> x >> y >> z;
			wuf.unite(x, y, z);
		}else{
			int x, y;
			cin >> x >> y;
			if(wuf.same(x, y)) cout << wuf.cost(x, y) << "\n";
			else cout << "?\n";
		}
	}
}