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;
typedef long long ll;

struct UnionFind{
  vector<int> parent;
  vector< ll > dist;
  UnionFind(int x=1){
    parent.clear();
    parent.resize(x,-1);
    dist.clear();
    dist.resize(x,0);
  }
  int find(int x){
    if(parent[x]<0)return x;
    int r=find(parent[x]);
    dist[x]+=dist[ parent[x] ];
    return parent[x]=r;    
  }
  ll depth(int x){
    find(x);
    return dist[x];
  }
  bool same(int x,int y){
    return (find(x)==find(y));
  }
  int size(int x){
    return -parent[find(x)];
  }
  void unite(int x,int y,ll k=0){
    k+=depth(y);
    k-=depth(x);
    k*=-1;
    x=find(x);
    y=find(y);
    if(x==y)return;
    if(size(x)<size(y)){
      swap(x,y);
      k*=-1;
    }
    parent[x]+=parent[y];
    parent[y]=x;
    dist[y]=k;
  }
};




int main(){
  int n,q;
  scanf("%d %d",&n,&q);
  UnionFind T(n);
  for(int i=0;i<q;i++){
    int type,x,y;
    scanf("%d %d %d",&type,&x,&y);
    if(type==0){
      int a;
      scanf("%d",&a);
      T.unite(x,y,a);
    }else{
      
      if(!T.same(x,y)){
        printf("?\n");
      }else{
        printf("%lld\n",T.depth(x)-T.depth(y));
      }
    }
  }
  return 0;
}