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 disjoinset {
	public:
		vector<int> rank,p,w;
	disjoinset (){}
	disjoinset(int size){
	rank.resize(size,0);
	p.resize(size,0);
	w.resize(size,0);
	for(int i=0; i<size;i++)makeSet(i);
	}
	void makeSet(int x){
	p[x] = x;
	rank[x] =0;
	w[x] = 0;
	}
	bool same(int x,int y){
	return findSet(x) == findSet(y);
	}
	void unite(int x,int y,int cost){
		int px = findSet(x);
		int py = findSet(y);
		link(px,py,cost-w[x]+w[y]);
	}
	void link(int x,int y,int cost){
		if(rank[x] > rank[y]){
		 p[y] = x;
		 w[y] = -cost;
		}else{
		 p[x] = y;
		 w[x] = cost;
		 if(rank[x]==rank[y] )rank[y]++;
		}
	}

	int rsum(int x){
		int sum = 0;
		int now = x;
		while(now!=p[now]){
			sum+=w[now];
			now=p[now];
		}
		return sum;
	}
	int findSet(int x){
		if(x!=p[x]){
		int tmp = findSet(p[x]);
		w[x]+=w[p[x]];
		p[x] = tmp;
		}
		return p[x];
	}

};
 
int main(){
	int n,a,b,c,q;
	int t;
	cin>>n>>q;
	disjoinset ds  = disjoinset(n);
	for(int i=0;i<q;i++){
		cin>>t;
		if(t==0){
		cin>>a>>b>>c;
		 ds.unite(a,b,c);
		}else if(t==1){
		cin>>a>>b;
		if(!ds.same(a,b) ) cout<<'?'<<endl;
		else {
			//cout<<ds.rsum(a)<<' '<<ds.rsum(b)<<endl;
			cout<<ds.rsum(a)-ds.rsum(b)<<endl;
			}
		}
	}

	return 0;
}