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 UnionFindTree{
private:
  vector<int> parent;
  vector<int> rank;
  vector<int> diff;
  
  int getRoot(int i){
    if(parent[i] == i)return i;

    int r = getRoot(parent[i]);
    diff[i] += diff[parent[i]];
    return parent[i] = r;
  }

  int weight(int x){
    getRoot(x);
    return diff[x];
  }

public:
  UnionFindTree(int n) : parent(n) , rank(n) , diff(n){
    for(int i=0; i<n; i++){ parent[i] = i; rank[i] = diff[i] = 0; }
  }

  void unite(int x, int y, int z){

    z += weight(x); z-= weight(y);
    
    x = getRoot(x);
    y = getRoot(y);
    
    if(x == y)return;
    if(rank[x] < rank[y]) swap(x,y) , z = -z;
    if(rank[x] == rank[y])rank[x]++;
    parent[y] = x;
    diff[y] = z;
  }

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

  int getDiff(int x, int y){
    return weight(y) - weight(x);
  }

};
  
int main(){

  int n,q;
  cin >> n >> q;
  UnionFindTree uft(n);

  for(int i=0; i<q; i++){
    int com, x, y, z;
    cin >> com >> x >> y;
    if(com == 0){
      cin >> z;
      uft.unite(x,y, z);
    }
    else{
      if( uft.same(x,y) ) cout << uft.getDiff(x,y) << endl;
      else cout << "?" << endl; 

    }
  }
    

  return 0;
}