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 LL = long long;
using namespace std;
class UnionFind{
private:
    vector<int> data;
    vector<LL> diff_weight;
public:
    UnionFind(int size) : data(size,-1), diff_weight(size, 0){}
    int root(int x){
        if(data[x] < 0){
            return x;
        }else{
            root(data[x]);
            diff_weight[x] += diff_weight[data[x]];
            return data[x] = root(data[x]);
        }
    }
    int weight(int x){
        root(x);
        return diff_weight[x];
    }
    bool connect(int x,int y, LL w){

        w += weight(x);w -= weight(y);
        x = root(x);y = root(y);
        if(x != y){
            if(data[x] > data[y])swap(x,y), w = -w;
            data[x] += data[y];data[y] = x;
            diff_weight[y] = w;
        }
        return x != y;
    }
    bool check(int x,int y){
        return root(x) == root(y);
    }
    int Size(int x){
        return -data[x];
    }
    int diff(int a, int b){
        return weight(b) - weight(a);
    }
};

int main(){
   int N,q;cin >> N >> q;
   UnionFind Uni(N);
   for(int a = 0;a < q;a++){
       int x;cin >> x;
       if(x == 0){
           int d,e,f;cin >> d >> e >> f;
           Uni.connect(d,e,f);
       }else{
           int d,e;cin >> d >> e;
           if(Uni.check(d,e))cout<<Uni.diff(d,e)<<endl;
           else cout<<"?"<<endl;
       }
   }
}