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;

const int error = 1e9;

class WeightedUnionFind{

private:
    vector<int> rank,p,d;

  public:
      WeightedUnionFind(){};
      WeightedUnionFind(int size){
        rank.resize(size,0);
        p.resize(size,0);
        d.resize(size,0);
        for(int i = 0; i < size; i++){
          p[i] = i;
        }
      }

    bool same(int x, int y){
      return  find(x) == find(y);
    }

    void relate(int x, int y, int z){
      int px = find(x);
      int py = find(y);
      link(px, py, d[y] + z - d[x]);
      find(x);
      find(y);
    }

    int find(int x){
      if(x != p[x]){
        int par = find(p[x]);
        d[x] += d[p[x]];
        p[x] = par;
      }
      return p[x];
    }

    int diff(int x, int y){
      find(x);
      find(y);
      if(same(x,y)){
        return d[x] - d[y];
      }else{
        return error;
      }
    }
private:
    void link(int x, int y, int z){
      if(rank[x] > rank[y]){
        p[y] = x;
        d[y] = -z;
      }else{
        p[x] = y;
        d[x] = z;
        if(rank[x] == rank[y]) rank[y]++;
      }
    }

};

int main(){
    int n, q;

    cin >> n >> q;
    WeightedUnionFind wuf = WeightedUnionFind(n);

    for(int i = 0; i < q; i++){
      int t, x, y, z;
      cin >> t;
      if(t == 0){
        cin >> x >> y >> z;
        wuf.relate(x, y, z);
      }else{
        cin >> x >> y;
        int ans = wuf.diff(x, y);
        if(ans == error)
          cout << "?" << endl;
        else
          cout << ans << endl;
      }
    }
    return 0;
}