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;
using ll = long long;

template <typename T>
struct WeightedUnionFind {
    vector<int> par, rank;
    vector<T> weight;

    WeightedUnionFind(int n) {
        par.resize(n);
        for (int i = 0; i < n; i++) par[i] = i;
        rank.resize(n);
        weight.resize(n);
    }

    int find(int x) {
        if (par[x] == x) return x;
        int r = find(par[x]);
        weight[x] += weight[par[x]];
        return par[x] = r;
    }

    bool unite(int x, int y, T w) {
        int rx = find(x), ry = find(y);
        w += weight[x] - weight[y];
        x = rx, y = ry;
        if (x == y) return false;

        if (rank[x] < rank[y]) swap(x, y), w = -w;

        if (rank[x] == rank[y]) rank[x]++;
        par[y] = x;
        weight[y] = w;
        return true;
    }

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

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

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int n, q;
    cin >> n >> q;
    WeightedUnionFind<int> wuf(n);
    for (int i = 0; i < q; i++) {
        int t;
        cin >> t;
        if (t == 0) {
            int x, y, z;
            cin >> x >> y >> z;
            wuf.unite(x, y, z);
        } else {
            int x, y;
            cin >> x >> y;
            if (wuf.same(x, y)) cout << wuf.diff(x, y) << '\n';
            else cout << "?\n";
        }
    }
}