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 namespace std;
using Int = long long;
//BEGIN CUT HERE
template <typename T>
struct WeightedUnionFind{
  T d;
  vector<int> r,p;
  vector<T> ws;

  WeightedUnionFind(){}
  WeightedUnionFind(int n,T d):
    d(d),r(n,1),p(n),ws(n,d){iota(p.begin(),p.end(),0);}

  int find(int x){
    if(x==p[x]) return x;
    int t=find(p[x]);
    ws[x]+=ws[p[x]];
    return p[x]=t;
  }

  T weight(int x){
    find(x);
    return ws[x];
  }

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

  void unite(int x,int y,T w){
    w+=weight(x);
    w-=weight(y);
    x=find(x);y=find(y);
    if(x==y) return;
    if(r[x]<r[y]) swap(x,y),w=-w;
    r[x]+=r[y];
    p[y]=x;
    ws[y]=w;
  }

  T diff(int x,int y){
    return weight(y)-weight(x);
  }
};
//END CUT HERE

signed DSL_1_B(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,q;
  cin>>n>>q;
  WeightedUnionFind<int> wuf(n,0);

  for(int i=0;i<q;i++){
    int t,x,y,z;
    cin>>t>>x>>y;
    if(t){
      if(wuf.same(x,y)) cout<<wuf.diff(x,y)<<"\n";
      else cout<<"?\n";
    }else{
      cin>>z;
      wuf.unite(x,y,z);
    }
  }
  cout<<flush;
  return 0;
}
/*
  verified on 2019/09/08
  http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DSL_1_B&lang=jp
*/

signed main(){
  DSL_1_B();
  return 0;
}