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>
using namespace std;
#include<vector>
template<typename T>
struct weightedUF{
	int n;
	vector<int>parent,rank;
	vector<T>dweight;
	weightedUF(int n_=0,T defvalue=0):n(n_),parent(n_),rank(n_,0),dweight(n_,defvalue)
	{
		for(int i=0;i<n;i++)parent[i]=i;
	}
	int find(int a)
	{
		if(parent[a]==a)return a;
		else
		{
			int ar=find(parent[a]);
			dweight[a]+=dweight[parent[a]];
			return parent[a]=ar;
		}
	}
	T weight(int a)
	{
		find(a);
		return dweight[a];
	}
	bool same(int a,int b)
	{
		return find(a)==find(b);
	}
	bool unite(int a,int b,int w)
	{
		w+=weight(a);w-=weight(b);
		a=find(a);b=find(b);
		if(a==b)return false;
		if(rank[a]<rank[b])
		{
			parent[a]=b;
			dweight[a]=-w;
		}
		else
		{
			parent[b]=a;
			dweight[b]=w;
			if(rank[a]==rank[b])rank[a]++;
		}
		return true;
	}
	T diff(int a,int b)
	{
		return weight(b)-weight(a);
	}
};
int main()
{
	int n,q;cin>>n>>q;
	weightedUF<int>P(n);
	for(int i=0;i<q;i++)
	{
		int c;cin>>c;
		if(c==0)
		{
			int x,y,w;cin>>x>>y>>w;P.unite(x,y,w);
		}
		else
		{
			int x,y;cin>>x>>y;
			if(P.same(x,y))cout<<P.diff(x,y)<<endl;
			else cout<<'?'<<endl;
		}
	}
}