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<algorithm>
#include<vector>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;
using namespace std;
#define N 100010
int n,q;
//int p[N],d[N];
class UnionFind{
private:
    int p[N],d[N];
    int Root(int x){
	int a=x,s=0;
	while(a!=p[a])s+=d[a],a=p[a];
	while(x!=a){int t=p[x];p[x]=a,s-=d[x],d[x]+=s,x=t;}
	return a;
    }
public:
    void Init(){
	lol(i,n)p[i]=i,d[i]=0;
    }
    void Unite(int a,int b,int c){
	int ra=Root(a),rb=Root(b);
	p[ra]=rb;
	d[ra]=c+d[b]-d[a];
    }
    int Query(int a,int b){
	int ra=Root(a),rb=Root(b);
	if(ra!=rb)return mod;
	return d[a]-d[b];
    }
};
int main(){
    cin>>n>>q;
    UnionFind uf;uf.Init();
    while(q--){
	int c;cin>>c;
	if(c==0){
	    int x,y,z;cin>>x>>y>>z;
	    uf.Unite(x,y,z);
	}
	if(c==1){
	    int x,y;cin>>x>>y;
	    int res=uf.Query(x,y);
	    if(res==mod)cout<<"?"<<endl;
	    else cout<<res<<endl;
	}
    }
    return 0;
}