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 i64=int64_t;
using namespace std;

#define int long long

struct wuf{
  vector<int> d;
  vector<int> p;
  wuf(int n):d(n, 0), p(n, -1){};
  int root(int x){
    if(p[x] < 0)return x;
    else{
      int r = root(p[x]);
      d[x] += d[p[x]];
      return p[x] = r;
    }
  }
  bool same(int x, int y){
    return root(x) == root(y); 
  }
  bool join(int x, int y, int w){
    w += weight(x);
    w -= weight(y);
    x = root(x);
    y = root(y);
    if(x == y)return false;
    if(p[x] > p[y]){
      swap(x, y);
      w = -w;
    }
    p[x] += p[y];
    p[y] = x;
    d[y] = w;
    return true;
  }
  int weight(int x){
    root(x);
    return d[x];
  }
  int diff(int x, int y){
    return weight(y) - weight(x);
  }
};

int32_t main() {
  int n, q;
  cin >> n >> q;
  wuf w(n);
  for(int i=0;i<q;i++){
    int c;
    cin >> c;
    int x, y, z;
    if(c == 0){
      cin >> x >> y >> z;
      w.join(x, y, z);
    }else{
      cin >> x >> y;
      if(w.same(x, y)){
        cout << w.diff(x, y) << endl;
      }else{
        cout << '?' << endl;
      }
    }
  }
}