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>
#include<climits>
using namespace std;

class Node{
public:
    int parent, rank, weight;
    Node(int id): parent(id), rank(0), weight(0){}
};

int find(vector<Node>& nodes, const int& x){
    if(nodes[x].parent != x){
        int new_parent = find(nodes, nodes[x].parent);
        if(new_parent != nodes[x].parent){
            nodes[x].weight += nodes[nodes[x].parent].weight;
        }
        nodes[x].parent = new_parent;
    }
    return nodes[x].parent;
}
void unite(vector<Node>& nodes, const int& x, const int& y, const int& z){
    int px = find(nodes, x), py = find(nodes, y);
    int pz = nodes[y].weight - nodes[x].weight + z;
    if(nodes[px].rank < nodes[py].rank){
        nodes[px].parent = py;
        nodes[px].weight = pz;
    }
    else if(nodes[py].rank < nodes[px].rank){
        nodes[py].parent = px;
        nodes[py].weight = -pz;
    }
    else{
        nodes[py].rank++;
        nodes[px].parent = py;
        nodes[px].weight = pz;
    }
}
int main(){
    int n, q, c, x, y, z; 
    cin >> n >> q;
    vector<Node> nodes;
    for(int i = 0; i < n; i++){
        nodes.push_back(Node(i));
    }
    for(int i = 0; i < q; i++){
        cin >> c;
        if(c == 0){
            cin >> x >> y >> z;
            unite(nodes, x, y, z);
        }
        else{
            cin >> x >> y;
            int px = find(nodes, x), py = find(nodes, y);
            if(px != py) cout << "?" << endl;
            else{
                cout << nodes[x].weight - nodes[y].weight << endl;
            }
        }
    }
}