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>
#define int long long
using namespace std;

const int INF = 1e10;

class WUF{
public:
  
  int n;
  vector<int> p, rank, w;
  
  WUF(){};
  WUF(int n):n(n),p(n),rank(n,0),w(n,0){ for(int i=0;i<n;i++) p[i] = i; };
  
  typedef pair<int,int> P;
  
  P find(int x){
    if( x != p[x] ){
      P r = find(p[x]);
      p[x] = r.first;
      w[x] += r.second;
      return P( p[x], w[x] );
    }
    return P( p[x], 0 );
  }
  
  void unite(int x, int y, int z){ // w[y] - w[x] = z
    P r1 = find(x);
    P r2 = find(y);
    x = r1.first;
    y = r2.first;
    int Wx = r1.second;
    int Wy = r2.second;
    if( rank[x] > rank[y] ){
      p[y] = x;
      w[y] = Wx - Wy + z;
    }
    else{
      p[x] = y;
      w[x] = Wy - Wx - z;
      if(rank[x]==rank[y]) rank[y]++;
    }

  }
  
  int diff(int x, int y){
    if( find(x).first != find(y).first ) return INF;
    return w[y] - w[x];
  }
  
};

signed main(){
  
  int n, q;
  cin>>n>>q;
  
  WUF wuf(n);
  
  while(q--){
    
    int flg;
    cin>>flg;

    if( flg == 0 ){
      
      int x, y, z;
      cin>>x>>y>>z;
      
      wuf.unite(x,y,z);
      
    }
    else{
      
      int x, y;
      cin>>x>>y;
      
      int ans = wuf.diff(x,y);

      if( ans == INF ) cout<<"?"<<endl;
      else cout<<ans<<endl;
      
    }
    
  }
  
  return 0;
}