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;

#define rep(i,n) for(int i = 0; i < (n); ++i)

template<class Abel> struct UnionFind {
	vector<int> par;
	vector<int> size;
	vector<int> rank;
	vector<Abel> diff_weight;

	UnionFind(int n) {
		init(n);
	}

	void init(int n) {
		par.resize(n);
		size.assign(n,1);
		rank.resize(n);
		diff_weight.resize(n);
		for (int i = 0; i < n; ++i) par[i] = i; 
	}

	int root(int x) {
		if (par[x] == x) {
			return x;
		} else { 
			int r = root(par[x]);
			size[x] = size[r];
			diff_weight[x] += diff_weight[par[x]];
			return par[x] = r;
		}
	}
	
	int scale(int x) {
		return size[root(x)];
	}

	Abel weight(int x) {
		root(x);
		return diff_weight[x];
	} 

	Abel diff(int x, int y) {
		return weight(y) - weight(x);
	} 

	bool is_same(int x, int y) {
		return root(x) == root(y);
	}

	bool merge(int x, int y, Abel w = 0) {
		w += weight(x);
		w -= weight(y);
		x = root(x);
		y = root(y);
		if (x == y) return false;
		if (rank[x] < rank[y]) {
			swap(x,y);
			w = -w;
		}
		if (rank[x] == rank[y]) ++rank[x];
		size[x] += size[y];
		par[y] = x;
		diff_weight[y] = w;
		return true;
	}
};
 

int main(){
	int n,q; cin >> n >> q;
	UnionFind<int> uf(n);
	rep(i,q){
		int x,y,z,t; cin >> t;
		if(t){
			cin >> x >> y;
			if(uf.is_same(x,y)) cout << uf.diff(x,y) << endl;
			else cout << "?\n";
		}else{
			cin >> x >> y >> z;
			uf.merge(x,y,z);
		}
	}
}