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;

vector<int> s, r, c;

void makeSet(int x){
    s.push_back(x);
    r.push_back(0);
    c.push_back(0);
}

int findSet(int x){
    int parent = s[x];
    if(x != s[x]) s[x] = findSet(s[x]);
    c[x] += c[parent];
    return s[x];
}

void relate(int x, int y, int z){
    int rootx = findSet(x);
    int rooty = findSet(y);
    if(rootx == rooty) return;
    z = z + c[x] - c[y];

    if(r[rootx] > r[rooty]){
        s[rooty] = rootx;
        c[rooty] = z;
    }else{
        s[rootx] = rooty;
        c[rootx] = -z;
        if(r[rootx] == r[rooty]){
            r[rooty] += 1;
        }
    }
}

void diff(int x, int y){
    if(findSet(x) == findSet(y)){
        cout << c[y] - c[x] << endl;
    }else{
        cout << "?" << endl;
    }
}

int main(){
    int n, q;
    cin >> n >> q;
    for(int i = 0; i < n; i++) makeSet(i);

    int com, x, y, z;
    for(int i = 0; i < q; i++){
        cin >> com;
        if(com == 0){
            cin >> x >> y >> z;
            relate(x, y, z);
        }else{
            cin >> x >> y;
            diff(x, y);
        }
    }



    return 0;
}