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 <iostream>
#include <vector>
using namespace std;
struct WeightedUnionFind{
  vector< pair<int, long long> > data;
  WeightedUnionFind(int n) : data(n, pair<int,long long>(-1,0LL)) {}
  bool unite(int x, int y, long long w){
    int x_ = find(x), y_ = find(y);
    if(x_ == y_) return true;
    if(data[y_].first < data[x_].first){
      swap(x_,y_); swap(x,y);
      w *= -1LL;
    }
    data[x_].first += data[y_].first;
    data[y_].first = x_;
    data[y_].second += w + rel_weight(x) - rel_weight(y);
    return true;
  }
  bool same(int x, int y){ return find(x) == find(y); }
  int find(int x){
    if(data[x].first < 0) return x;
    int p = find(data[x].first);
    data[x].second += data[data[x].first].second;
    data[x].first = p;
    return data[x].first;
  }
  long long rel_weight(int x){
    return data[x].second;
  }
};
int main(){
  int n, q;cin >> n >> q;
  WeightedUnionFind wuf(n);
  while(q--){
    int t, x, y, z;cin >> t >> x >> y;
    if(t){
      if(wuf.same(x,y)) cout << wuf.rel_weight(y) - wuf.rel_weight(x) << endl;
      else cout << "?" << endl;
      continue;
    }
    cin >> z;
    wuf.unite(x,y,z);
  }
}