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:
        vector<int> rnk, par, weight;
          
        DisjointSet(){}
        DisjointSet(int size){
            rnk.resize(size, 0);
            par.resize(size, 0);
            weight.resize(size, 0);
            for(int i = 0; i < size; i++) makeSet(i);
        }
  
        void makeSet(int x){
            par[x] = x;
            rnk[x] = 0;
            weight[x] = 0;
        }
  
        bool same(int x, int y){
            return find(x) == find(y);
        }
  
        void unite(int x, int y, int z){
            par[x] = find(x);
            par[y] = find(y);
            int add = z - (weight[y] - weight[x]);
            if(rnk[par[x]] > rnk[par[y]]){
                weight[par[y]] = add;
                par[par[y]] = par[x];
            }else{
                weight[par[x]] = -add;
                par[par[x]] = par[y];
                if(rnk[par[x]] == rnk[par[y]]){
                	rnk[par[y]]++;
                }
            }
        }
          
        int diff(int x, int y){
            return weight[y] - weight[x];
        }
  
        int find(int x){
            if(x != par[x]){
                int t = find(par[x]);
                weight[x] += weight[par[x]];
                return par[x] = t;
            }
            else return x;
        }
};
  
int main(){
    int n, q;
    cin >> n >> q;
    DisjointSet UF(n);
    for(int i = 0; i < q; i++){
        int query;
        cin >> query;
        if(query == 0){
            int x, y, z;
            cin >> x >> y >> z;
            if(UF.same(x, y)) continue;
            UF.unite(x, y, z);
            //for(int j = 0; j < n; j++) cout << UF.weight[j] << (j == n - 1 ? '\n' : ' ');
        }else{
            int x, y;
            cin >> x >> y;
            if(UF.same(x, y)){
                cout << UF.diff(x, y) << endl;
            }else{
                cout << '?' << endl;
            }
        }
    }
    return 0;
}