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 WeightedDisjointSet{
public:
    vector<int> p,rank,depth;
    
    WeightedDisjointSet();
    WeightedDisjointSet(int size){
        // サイズをセットし直す
        rank.resize(size,0);
        p.resize(size,0);
        depth.resize(size,0);
        for(int i = 0;i < size;++i){
            makeSet(i);
        }
    }
    
    // 要素xがただ一つである集合を作る
    void makeSet(int x){
        p[x] = x;
        rank[x] = 0;
        depth[x] = 0;
    }
    
    // 同じ集合にいるか
    bool same(int x,int y){
        return findSet(x) == findSet(y);
    }
    
    void relate(int x, int y, int z){
        int px = findSet(x);
        int py = findSet(y);
        link(px,py,depth[y] + z - depth[x]);
    }
    
    // 要素xが属する集合の代表の要素を求める
    int findSet(int x){
        // 自身がルートでない場合
        if(x != p[x]){
            // 自身の親をさかのぼる
            int tmp = findSet(p[x]);
            depth[x] += depth[p[x]];
            p[x] = tmp;
        }
        return p[x];
    }
    
    void link(int x, int y, int z){
        if(rank[x] > rank[y]){
            p[y] = x;
            depth[y] = -z;
        }else{
            p[x] = y;
            depth[x] = z;
            if(rank[x] == rank[y]){
                rank[y]++;
            }
        }
    }

    int diff(int x, int y){
        return sumDepth(x) - sumDepth(y);
    }
    
    int sumDepth(int x){
        int sum = 0;
        int index = x;
        while(index != p[index]){
            sum += depth[index];
            index = p[index];
        }
        return sum;
    }
};

int main(void){
    int n,q,c,x,y,z;
    cin >> n >> q;
    WeightedDisjointSet wds = WeightedDisjointSet(n);
    
    for(int i = 0;i < q;++i){
        cin >> c >> x >> y;
        switch(c){
                // relate
            case 0:{
                cin >> z;
                wds.relate(x, y, z);
                break;
            }
                // diff
            case 1:{
                if(!wds.same(x, y)){
                    cout << "?" << endl;
                }
                else{
                    cout << wds.diff(x, y) << endl;
                }
                break;
            }
        }
    }
}