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;

constexpr int MX = 100005;
int rnk[MX];
int w_diff[MX];
int root[MX];

int find(int x){
  if (x == root[x]) return x;
  int r = find(root[x]);
  w_diff[x] += w_diff[root[x]];
  return root[x] = r;
}

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

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

void merge(int x, int y, int w){
    
    w += weight(x);
    w -= weight(y);

    x = find(x);
    y = find(y);
    
    if (x == y) return;
    
    if(rnk[x] < rnk[y]) swap(x, y),  w = -w;
    if(rnk[x] == rnk[y]) ++rnk[x];
    root[y] = x;
    w_diff[y] = w;
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    
    int n, q;
    cin >> n >> q;
    
    for(int i=0; i<n; i++) {
        rnk[i]=0;
        w_diff[i]=0;
        root[i]=i;
    }
 
    for(int i=0; i<q; i++){
        int c, x, y, z;
        cin >> c;
        if(c == 0){
            cin >> x >> y >> z;
            merge(x, y, z);
        }else if (c == 1){
            cin >> x >> y;
            if (find(x) != find(y)){
                cout << "?" << endl;
            }else{
                cout << diff(x, y) << endl;   
            }
        }
    }
    cout << flush;
    return 0;
}