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;
#define rep(i,n) for (int (i)=(0);(i)<(int)(n);++(i))
using ll = long long;
using P = pair<int, int>;
using namespace std;


// 重み付きUnionFind
// Atcoder People on a Line で Verfty
struct WeightUnionFind {
    static const int Max = 101010;
    int par[Max];
    int ws[Max];

    void init(int n) {
        for (int i = 0; i < n; ++i) {
            par[i] = -1;
        }
    }

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

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

    void unite(int x, int y, int w) {
        w += weight(x);
        w -= weight(y);
        x = find(x);
        y = find(y);
        if (x == y) return;
        if (par[y] < par[x]) {
            int tmp = x;
            x = y;
            y = tmp;
            w = -w;
        }
        par[x] += par[y];
        par[y] = x;
        ws[y] = w;
    }

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

    int diff(int x, int y) {
        if (!same(x, y)) return -1e8;
        return weight(y) - weight(x);
    }
    int size(int x) {
        return -par[find(x)];
    }
};

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

    WeightUnionFind uf;
    uf.init(n);

    rep(i, q) {
        int t, x, y, z;
        cin >> t >> x >> y;
        if (t == 0) cin >> z;

        if (t == 0) {
            uf.unite(x, y, z);
        }
        else {
            if (uf.same(x, y)) {
                cout << uf.diff(x, y) << endl;
            }
            else {
                cout << "?" << endl;
            }
        }
    }

    return 0;
}