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 <typename T>
class weighted_union_find {
public:
    weighted_union_find(size_t n)
    :par(n, -1), weight_diff(n, 0) {}

    // weight(y) - weight(x) = w
    bool unite(int x, int y, T w) {
        w += weight(x);
        w -= weight(y);

        if((x = find(x)) == (y = find(y))) {
            return false;
        } else {
            if(par[y] < par[x]) {
                swap(x, y);
                w = -w;
            }
            par[x] += par[y];
            par[y] = x;
            weight_diff[y] = w;
            return true;
        }
    }

    int find(int x) {
        if(par[x] < 0) {
            return x;
        } else {
            int root = find(par[x]);
            weight_diff[x] += weight_diff[par[x]];
            return par[x] = root;
        }
    }

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

    T diff(int x, int y) {
        return weight_diff[y] - weight_diff[x];
    }

    int size(int x) {
        return -par[find(x)];
    }

private:
    vector<int> par;
    vector<T> weight_diff;
};


int main() {
    int n, q; cin >> n >> q;
    weighted_union_find<int> uf(n);

    while(q--){
        int k; cin >> k;
        if(k == 0) {
            int x, y, z;
            cin >> x >> y >> z;
            uf.unite(x, y, z);
        } else {
            int x, y;
            cin >> x >> y;
            if(uf.find(x) != uf.find(y)) cout << '?' << endl;
            else cout << uf.diff(x, y) << endl;
        }
    }
}