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 int long long
using lint=long long;

struct wUF{
	int n;
	vector<int>pr;
	vector<lint>df;
	wUF(){};
	wUF(int n_){
		n=n_;
		pr.resize(n,-1);
		df.resize(n,0);
	};
	int root(int x){
		if(pr[x]<0)return x;
		else{
			 int r=root(pr[x]);
			df[x]+=df[pr[x]];
			return pr[x]=r;
		}
	}
	void unify(int x,int y,lint w){
		w+=depth(x)-depth(y);
		x=root(x),y=root(y);
		if(x==y)return;
		if(size(x)<size(y)){swap(x,y);w=-w;}
		pr[x]+=pr[y];
		pr[y]=x;
		df[y]=w;
	}
	int size(int x){return -pr[root(x)];}
	bool same(int x,int y){return root(x)==root(y);}
	lint depth(int x){root(x);return df[x];}
	lint dist(int x,int y){return depth(y)-depth(x);}
};

signed main(){
	int n,q;cin>>n>>q;
	wUF wuf(n);
	while(q--){
		int c,x,y;
		lint z;
		cin>>c>>x>>y;
		if(c==0){ 
			cin>>z;
			wuf.unify(x,y,z);
		}else{
			if(!wuf.same(x,y))cout<<"?"<<endl;
			else cout<<wuf.dist(x,y)<<endl;
		}		
	}
}