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;
struct weighted_disjoint_set{
    vector<pair<int, int>> p;
    weighted_disjoint_set(int n){
        p.resize(n);
        for(int i = 0; i < n; i += 1) p[i] = {i, 0};
    }
    pair<int, int> fp(int u){
        if(u == p[u].first) return p[u];
        auto ppu = fp(p[u].first);
        return p[u] = {ppu.first, p[u].second + ppu.second};
    }
    //a[u] + w = a[v]
    void relate(int u, int v, int w){
        auto pu = fp(u), pv = fp(v);
        p[pu.first] = {pv.first, pv.second + w - pu.second};
    }
    bool diff(int u, int v, int& w){
        auto pu = fp(u), pv = fp(v);
        if(pu.first != pv.first) return false;
        return w = pu.second - pv.second, true;
    }
};
int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    int n, q;
    cin >> n >> q;
    weighted_disjoint_set wds(n);
    for(int i = 0; i < q; i += 1){
        int com, u, v, w;
        cin >> com >> u >> v;
        if(com){
            if(not wds.diff(u, v, w)) cout << "?\n";
            else cout << w << "\n";
        }
        else{
            cin >> w;
            wds.relate(u, v, w);
        }
    }
    return 0;
}