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;
#define int long long
const int INF = 1LL << 31;

struct UF{
  const int N = 1e5+10;
  vector<int> par;
  vector<int> depth;
  vector<int> diff;

  void init(int n){
    par.resize(n); depth.resize(n); diff.resize(n);
    for(int i = 0; i < n; i++){
      par[i] = i;
      depth[i] = 0;
      diff[i] = 0;
    }
  }

  //木の根を求める
  int find(int x){
    if(par[x] == x){
      return x;
    }
    else {
      int r = find(par[x]);
      diff[x] += diff[par[x]];
      return par[x] = r;
    }
  }

  int weight(int x){
    find(x); //経路圧縮
    return diff[x];
  }

  //xとyの属する集合を併合
  void unite(int x,int y,int w){
    w += weight(x) - weight(y);
    x = find(x);
    y = find(y);
    if(x == y) return;

    if(depth[x] < depth[y]) swap(x,y),w = -w;
    if(depth[x] == depth[y]) depth[x]++;
    par[y] = x;
    diff[y] = w;
  }
}uf;

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

  int n,q; cin >> n >> q;
  uf.init(n);
  vector<int> v;
  for(int i = 0; i < q; i++){
    int k,x,y,z; cin >> k;
    if(k){
      cin >> x >> y;
      if(uf.find(x) != uf.find(y)) v.push_back(INF);
      else v.push_back(uf.weight(y) - uf.weight(x));
    }
    else {
      cin >> x >> y >> z;
      uf.unite(x,y,z);
    }
  }

  for(auto p : v){
    if(p == INF) cout << '?' << endl;
    else cout << p << endl;
  }

  return 0;
}