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 <stdio.h>

namespace beet{
  
  template<typename T>
  void swap(T &a,T &b){
    T x=a;
    a=b;
    b=x;
  }

  const int MAX = 1e5+10;
  struct UnionFind{
    int r[MAX],p[MAX],w[MAX];
    UnionFind(int n){
      for(int i=0;i<n;i++){
        r[i]=1;
        p[i]=i;
        w[i]=0;
      }    
    }
    int find(int x){
      if(p[x]==x){
        return x;
      }
      int t=find(p[x]);
      w[x]+=w[p[x]];
      return p[x]=t;
    }
    int same(int x,int y){
      return find(x)==find(y);
    }
    int weight(int x){
      find(x);
      return w[x];
    }
    void unite(int x,int y,int d){
      d+=weight(x);
      d-=weight(y);
      x=find(x);y=find(y);
      if(x==y) return;
      if(r[x]<r[y]) swap(x,y),d=-d;
      r[x]+=r[y];
      p[y]=x;
      w[y]=d;
    }
    int diff(int x,int y){
      return weight(y)-weight(x);
    }
  };
}
using namespace beet;

int main(){
  int n,q;
  scanf("%d %d",&n,&q);
  UnionFind uf(n);
  while(q--){
    int t,x,y;
    scanf("%d %d %d",&t,&x,&y);
    if(t==0){
      int z;
      scanf("%d",&z);
      uf.unite(x,y,z);
    }    
    if(t==1){
      if(uf.same(x,y)){
        printf("%d\n",uf.diff(x,y));
      }else{
        puts("?");
      }
    }
  }  
  return 0;
}