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;
template <typename T>
struct weighted_unionfind{
	vector<int> p;
	vector<T> d;
	weighted_unionfind(int N){
		p = vector<int>(N, -1);
		d = vector<T>(N, 0);
	}
	int root(int x){
		if (p[x] == -1){
			return x;
		} else {
			root(p[x]);
			d[x] = d[x] + d[p[x]];
			p[x] = root(p[x]);
			return p[x];
		}
	}
	bool same(int x, int y){
		x = root(x);
		y = root(y);
		return x == y;
	}
	void unite(int x, int y, T t){
		root(x);
		root(y);
		t = t + d[y] - d[x];
		x = root(x);
		y = root(y);
		if (x != y){
			p[x] = y;
			d[x] = t;
		}
		return;
	}
};
int main(){
  int n, q;
  cin >> n >> q;
  weighted_unionfind<long long> UF(n);
  for (int i = 0; i < q; i++){
    int t;
    cin >> t;
    if (t == 0){
      int x, y;
      long long z;
      cin >> x >> y >> z;
      if (!UF.same(x, y)){
        UF.unite(x, y, z);
      }
    }
    if (t == 1){
      int x, y;
      cin >> x >> y;
      if (UF.same(x, y)){
        cout << UF.d[x] - UF.d[y] << endl;
      } else {
        cout << '?' << endl;
      }
    }
  }
}