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 ll=long long;
using ull=unsigned long long;
using pii=pair<int,int>;

#define INF LONG_MAX
#define MOD 1000000007
#define rng(a) a.begin(),a.end()
#define rrng(a) a.end(),a.begin()

struct weightUF{
  vector<int>par,rank;
  vector<ll>diff_weight;

  weightUF(int n){
    par.resize(n);
    rank.resize(n,0);
    diff_weight.resize(n,0);
    for(int i=0;i<n;i++)par[i]=i;
  }
  int root(int x){
    if(par[x]==x)return x;
    else{
      int r=root(par[x]);
      diff_weight[x]+=diff_weight[par[x]];
      return par[x]=r;
    }
  }
  ll weight(int x){
    root(x);
    return diff_weight[x];
  }
  bool is_same(int x,int y){
    return root(x)==root(y);
  }
  bool unite(int x,int y,ll w){
    w+=weight(x);
    w-=weight(y);
    x=root(x);
    y=root(y);
    if(x==y)return false;
    if(rank[x]<rank[y])swap(x,y),w=-w;
    if(rank[x]==rank[y])++rank[x];
    par[y]=x;
    diff_weight[y]=w;
    return true;
  }
  ll diff(int x,int y){
    return weight(y)-weight(x);
  }
};

int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);

  int n,q; cin>>n>>q;
  weightUF uf(n);
  for(int i=0;i<q;i++){
    int query;
    cin>>query;
    if(query==0){
      int x,y,z;
      cin>>x>>y>>z;
      uf.unite(x,y,z);
    }
    else{
      int x,y;
      cin>>x>>y;
      ll res=uf.diff(x,y);
      if(uf.is_same(x,y))cout<<res<<endl;
      else cout<<'?'<<endl;
    }
  }
  return 0;
}