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<vector>
using namespace std;


class union_find
{
	int  _setnum;
	vector<int> par, nume, diff_weight;
public:
	union_find(){
	}
	
	union_find(int x){
		par.resize(x);
		nume.resize(x);
		diff_weight.resize(x);
		init();
	}
	
	~union_find(){
		//
		
	}
	
	void clear(){
		_setnum = 0;
		par.clear();
		nume.clear();
		diff_weight.clear();
	}
	
	void init(){
		_setnum = par.size();
		for(int i = 0; i < par.size(); i++){
			par[i] = i;
			nume[i] = 1;
			diff_weight[i] = 0;
		}
	}
	
	void resize(int x){
		
		par.resize(x);
		nume.resize(x);
		diff_weight.resize(x);
		init();
	}

	int find(int x){
		if(par[x] == x) {
				return x;
		} else {
			int p = find(par[x]);
			
			diff_weight[x] += diff_weight[par[x]];
			
			return par[x] = p;
		}
	}
	
	// weight(y) - weight(x) = w
	void unite(int x, int y, int w){
		
		w = -w;
		
		w -= weight(x);
		w += weight(y);
		
		x = find(x);
		y = find(y);
	
		if(x == y)return;
		
		_setnum--;
		
		if(nume[x] > nume[y]) std::swap(x,y), w = -w;
		
		par[x] = y;
		
		nume[y] += nume[x];
		
		diff_weight[x] = w;
	}
	
	int weight(int x){
		find(x);
		
		return diff_weight[x];
	}
	
	// find(x) == find(y)
	int diff(int x, int y){
		return weight(y) - weight(x);
	}
	
	bool same(int x, int y){
		return find(x) == find(y);
	}
	
	int numel(int x){
		return nume[find(x)];
	}
	
	int size(){
		return par.size();
	}
	
	int setnum(){
		return _setnum;
	}
};

signed main(){
	
	int n, q;
	union_find uf;
	
	cin>>n>>q;
	
	uf.resize(n);
	
	for(int i = 0; i < q; i++){
		int num, x, y, z;
		
		cin>>num;
		
		if(num == 0) {
			cin>>x>>y>>z;
			
			uf.unite(x, y, z);
			
		} else if(num == 1) {
			cin>>x>>y;
			
			if(uf.same(x, y)) {
				cout<<uf.diff(x, y)<<endl;
			} else {
				cout<<"?"<<endl;
			}
		}
	}
	
	return 0;
}