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 rep(i,n) for(int i = 0; i < (int)n; i++)

class Potential_Union_Find{
  vector<int> par; vector<int> rank; vector<int> diff_weight;
public:
  Potential_Union_Find(int n) {
    par.assign(n,0); rank.assign(n,0); diff_weight.assign(n,0);
    rep(i,n) par[i] = i;
  }
  int find(int x) {
    if(par[x] == x) {
      return x;
    } else {
      int r = find(par[x]);
      diff_weight[x] += diff_weight[par[x]];
      return par[x] = r;
    }
  }
  int weight(int x){
    find(x);
    return diff_weight[x];
  }
  void unite(int x, int y, int w){
    w += weight(x); w -= weight(y);
    x = find(x); y = find(y);
    if(x == y) return;
    if(rank[x] < rank[y]) swap(x,y), w = -w;
    if(rank[x] == rank[y]) rank[x]++;
    par[y] = x;
    diff_weight[y] = w;
  }
  bool same(int x, int y){
    return find(x) == find(y);
  }
  int diff(int x, int y){
    return weight(y) - weight(x);
  }
};

int main() {
  int n, q;
  cin >> n >> q;
  Potential_Union_Find puf(n);
  rep(i,q) {
    int t;
    cin >> t;
    if(t == 0) {
      int x, y, z;
      cin >> x >> y >> z;
      puf.unite(x,y,z);
    } else {
      int x, y;
      cin >> x >> y;
      if(puf.same(x,y)) cout << puf.diff(x,y) << endl;
      else cout << "?" << endl;
    }
  }
  return 0;
}