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 <class Abel>
class UnionFind{
    vector<int> par_, weight_;
public:
    UnionFind(size_t n){
        par_.assign(n, -1);
        weight_.assign(n, 0);
    }

    int root(int x){
        if (par_[x] < 0) {
            return x;
        }else{
            int res = root(par_[x]);
            weight_[x] += weight_[par_[x]];
            return par_[x] = res;
        }
    }

    int weight(int x){
        root(x);
        return weight_[x];
    }

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

    int size(int x){
        return -par_[root(x)];
    }

    bool IsSame(int x, int y){
        return root(x) == root(y);
    }

    void Merge(int x, int y, Abel w){
        w += weight(x);
        w -= weight(y);
        x = root(x);
        y = root(y);
        if (IsSame(x, y))
            return;
        if (size(x) < size(y)) {
            w = -w;
            swap(x, y);
        }
        par_[x] += par_[y];
        par_[y] = x;
        weight_[y] = w;
    }
};

int main(){
    int n, m;
    cin >> n >> m;
    UnionFind<int> uf(n);
    for (int i = 0; i < m; i++) {
        int q, l, r, d;
        cin >> q;
        if (q == 0) {
            cin >> l >> r >> d;
            uf.Merge(l, r, d);
        }else{
            cin >> l >> r;
            cout << ((uf.IsSame(l, r)) ? to_string(uf.weight(l, r)) : "?") << endl;
        }
    }

    return 0;
}