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 <numeric>
#include <vector>

template <class T>
class WeightedUnionFind {
public:
    std::vector<int> par, num;
    std::vector<T> dist;  // A[par[v]] - A[v] = dist[v]

    explicit WeightedUnionFind(int N)
        : par(N), num(N, 1), dist(N, 0) {
        iota(par.begin(), par.end(), 0);
    }

    int find(int v) {
        if (par[v] == v) {
            return v;
        } else {
            int p = find(par[v]);
            dist[v] += dist[par[v]];
            return par[v] = p;
        }
    }

    // A[u] - A[v] = d
    void unite(int u, int v, T d) {
        find(u), find(v);
        d += dist[u];
        d -= dist[v];
        u = par[u], v = par[v];
        if (u == v) return;

        if (num[u] < num[v]) {
            std::swap(u, v);
            d = -d;
        }

        num[u] += num[v];
        par[v] = u;
        dist[v] = d;
    }

    // A[v] - A[u]
    T diff(int u, int v) {
        find(u), find(v);
        return dist[u] - dist[v];
    }

    bool same(int u, int v) { return find(u) == find(v); }
    bool ispar(int v) { return v == find(v); }
    int size(int v) { return num[find(v)]; }
};

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    int N, Q;
    std::cin >> N >> Q;
    WeightedUnionFind<long long> wuf(N);
    for (int q = 0; q < Q; ++q) {
        int t, u, v;
        std::cin >> t >> u >> v;
        if (t == 0) {
            long long d;
            std::cin >> d;
            wuf.unite(v, u, d);
        } else {
            if (!wuf.same(u, v)) {
                std::cout << "?\n";
            } else {
                std::cout << wuf.diff(u, v) << '\n';
            }
        }
    }
    return 0;
}