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 DisjointSet {

public:
	int size;
	vector<int> p, w, r;
	
	DisjointSet(){}
	DisjointSet(int n){
		size = n;
		p.resize(size, 0);
		r.resize(size, 0);
		w.resize(size, 0);
		for(int i=0;i<size;i++){
			makeSet(i);
		}
	}

	void makeSet(int x){
		p[x]=x;
		r[x]=0;
		w[x]=0;	
	}
	
	void relate(int x, int y, int z){
		int xp = findSet(x);
		int yp = findSet(y);
		link(xp, yp, z-w[x]+w[y]);
	}

	void link(int x, int y, int cost){
		if(r[x]>r[y]){
			p[y]=x;
			w[y]-=cost;
		} else {
			p[x]=y;
			w[x]+=cost;
			if(r[x]==r[y]){
				r[y]++;
			}
		}
	}
	
	bool same(int x, int y){
		return findSet(x)==findSet(y);
	}
	
	int sum(int x){
		int sum=0;
		int cur=x;
		while(cur!=p[cur]){
			sum+=w[cur];
			cur=p[cur];
		}
		return sum;
	}
	
	int findSet(int x){
		if(p[x]!=x){
			int tmp=findSet(p[x]);
			w[x]+=w[p[x]];
			p[x]=tmp;
		}
		return p[x];
	}
};

int main(){
	int n, q;
	cin >> n >> q;
	DisjointSet ds(n);
	for (int i=0;i<q;i++) {
		int c, x, y, z;
		cin >> c >> x >> y;
		if (c == 0) {
			cin >> z;
			ds.relate(x, y, z);
		} else {
			if (!ds.same(x, y)){
				cout << "?" << endl;
			} else {
				int sumX = ds.sum(x);
				int sumY = ds.sum(y);
				cout << sumX - sumY << endl;
			}
		}
	}
	return 0;
}