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 F = std::plus<T>, class F_INV = std::minus<T>, const T I = 0>
struct WeightedUnionFindTree {
    const F op = F(); const F_INV op_inv = F_INV();
    vector<int> par, rnk; vector<T> wt;
    void build(int n) { par.assign(n, -1); rnk.assign(n, 0); wt.assign(n, I); }
    int find(int x) {
        if (par[x] < 0) return x;
        int r = find(par[x]);
        wt[x] = r == par[x] ? wt[x] : op(wt[par[x]], wt[x]);
        return par[x] = r;
    }
    bool same(int x, int y) { return find(x) == find(y); }
    int size(int x) { return -par[find(x)]; }
    T eval(int x) { find(x); return wt[x]; }
    T diff(int x, int y) { assert(same(x, y)); return op_inv(wt[y], wt[x]); }
    bool unite(int x, int y, T d) {
        d = op_inv(op(wt[x], d), wt[y]);
        if ((x = find(x)) == (y = find(y))) return 0;
        rnk[x] = max(rnk[x], rnk[y] + 1);
        wt[y] = d;
        par[x] += par[y];
        par[y] = x;
        return 1;
    }
    bool uniteByRank(int x, int y, T d) {
        return rnk[find(x)] < rnk[find(y)] ? unite(y, x, op_inv(I, d)) : unite(x, y, d);
    }
};

int main() {
    int n, q;
    cin >> n >> q;
    vector<int> x(q), y(q), z(q, -1);
    for (int i = 0; i < q; ++i) {
        int t;
        cin >> t;
        if (t == 0) cin >> x[i] >> y[i] >> z[i];
        else cin >> x[i] >> y[i];
    }

    WeightedUnionFindTree<int> wuf;
    wuf.build(n);

    for (int i = 0; i < q; ++i) {
        if (z[i] != -1) wuf.uniteByRank(x[i], y[i], z[i]);
        else if (wuf.same(x[i], y[i])) cout << wuf.diff(x[i], y[i]) << endl;
        else cout << "?" << endl;
    }
}