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<algorithm>
#include<vector>
#include<map>
#include<set>
#include<string>
#include<queue>
#include<stack>
#include<numeric>
using namespace std;
#define INF (1 << 30) - 1
#define LINF 1LL << 60
const int MOD = 1000000007;
using ll = long long;
using P = pair<int, int>;

struct UnionFind{
  vector<int> p;
  vector<ll> weight;
  UnionFind(int n){
    p.resize(n, -1);
    weight.resize(n, 0);
  }

  int find(int x){
    if(p[x] == -1)return x;
    else{
      int r = find(p[x]); 
      weight[x] += weight[p[x]]; 
      return p[x] = r;
    }
  }

  ll get_weight(int x){
    find(x);
    return weight[x];
  }

  void unite(int x, int y, ll w){
    w += get_weight(x); 
    w -= get_weight(y); 

    x = find(x);
    y = find(y);
    if(x == y)return;
    p[y] = x;
    weight[y] = w;
  }

  ll diff(int x, int y){
    return get_weight(y) - get_weight(x);
  }
};

int main(){
  int n, q;
  cin >> n >> q;
  UnionFind uf(n);
  for(int i = 0; i < q; ++i){
  	int com, x, y;
  	ll z;
  	cin >> com;
  	if(com == 0){
  		cin >> x >> y >> z;
  		uf.unite(x, y, z);
  	}
  	else{
  		cin >> x >> y;
  		if(uf.find(x) == uf.find(y)){
  			cout << uf.diff(x, y) << endl;
  		}
  		else cout << "?" << endl;
  	}
  }
  
  return 0;
}