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 <vector>
#include <algorithm>
#include <cassert>
#include <string>
using namespace std;

struct QuickFind {
    vector<int> i2g;
    vector< vector<int> > g2i;
    vector<long long int> weight;
    int N;

    QuickFind(int N_) {
        N = N_;
        i2g.resize(N); g2i.resize(N);
        weight.resize(N);

        for(int i=0; i<N; i++) {
            i2g[i] = i;
            g2i[i] = vector<int>{i};
        }
    }

    bool same(int u, int v) {
        return i2g[u] == i2g[v];
    }

    long long int query(int u, int v) {
        assert(same(u, v));
        return weight[v] - weight[u];
    }

    void merge(int u, int v, int w) {
        if(same(u, v)) return;
        int ru = i2g[u], rv = i2g[v];

        if(g2i[rv].size() > g2i[ru].size()) {
            swap(ru, rv); swap(u, v);
            w = -w;
        }

        long long int prev = weight[v];
        weight[v] = weight[u] + w;

        for(auto e : g2i[rv]) {
            i2g[e] = ru;
            g2i[ru].push_back(e);
            if(e == v) continue;
            int diff = weight[e] - prev;
            weight[e] = weight[v] + diff;
        }

        g2i[rv].clear();
    }
};

int main() {
    int N, Q; cin >> N >> Q;
    QuickFind qf(N);
    for(int i=0; i<Q; i++) {
        int query; cin >> query;
        if(query == 0) {
            int u, v, w; cin >> u >> v >> w;
            qf.merge(u, v, w);
        }
        else {
            int u, v; cin >> u >> v;
            if(qf.same(u, v)) cout << qf.query(u, v) << endl;
            else cout << "?" << endl;
        }
    }
    return 0;
}