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>
struct WeightedUnionFind {
    unsigned int n;
    T d;
    vector<int> r, p;
    vector<T> ws;

    WeightedUnionFind() = default;

    WeightedUnionFind(unsigned int sz, T d_) :
            n(sz), d(d_), r(n, 1), p(n), ws(n, d) { iota(p.begin(), p.end(), 0); }

    int find(int x) {
        if (x == p[x]) {
            return x;
        } else {
            int t = find(p[x]);
            ws[x] += ws[p[x]];
            return p[x] = t;
        }
    }

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

    bool same(int x, int y) {
        return find(x) == find(y);
    }

    void unite(int x, int y, T w) {
        w += weight(x);
        w -= weight(y);
        x = find(x);
        y = find(y);
        if (x == y) return;
        if (r[x] < r[y]) swap(x, y), w = -w;
        r[x] += r[y];
        p[y] = x;
        ws[y] = w;
    }

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


int main() {
    unsigned int n, q;
    cin >> n >> q;

    auto wuf = WeightedUnionFind<int>(n, 0);

    for (int i = 0; i < q; ++i) {
        int op, x, y;
        cin >> op >> x >> y;

        if (op == 0) {
            int z;
            cin >> z;
            wuf.unite(x, y, z);
        } else {
            if (wuf.same(x, y)) {
                cout << wuf.diff(x, y) << endl;
            } else {
                cout << "?" << endl;
            }
        }
    }
    return 0;
}