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>
#define rep(i, n) for (int i = 0; i < (n); ++i) 
#define PI acos(-1)

using namespace std;
using ll = long long;
using P = pair<int, int>;
using LP = pair<ll, ll>;

struct DisjointSet {
    private:
        vector<int> par;
        vector<int> diff_weight;
        vector<int> rank;
    
    public:
        DisjointSet(int n) {
            par = vector<int>(n);
            rep(i, n) par[i] = i;
            diff_weight = vector<int>(n);
            rank = vector<int>(n);
        }
    
        int find(int i) {
            if (par[i] == i) return i;
            int p = find(par[i]);
            diff_weight[i] += diff_weight[par[i]];
            par[i] = p;
            return p;
        }

        int weight(int i) {
            int p = find(i);
            return diff_weight[i];
        }
    
        bool joint(int i, int j, int w) {
            w += weight(i); w -= weight(j);
            int pi = find(i);
            int pj = find(j);
            if (pi == pj) return false;
    
            if (rank[pi] < rank[pj]) {
                swap(pi, pj);
                w = -w;
            }
            if (rank[pi] == rank[pj]) rank[pj]++;

            par[pj] = pi;
            diff_weight[pj] = w;
            return true;
        }
    };

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

    int n, q;
    cin>>n>>q;
    DisjointSet ds(n);
    rep(i, q) {
        int c, x, y, z;
        cin>>c>>x>>y;
        if (c == 0) {
            cin>>z;
            ds.joint(x, y, z);
        }
        else {
            int px = ds.find(x);
            int py = ds.find(y);
            if (px != py) cout<<'?'<<endl;
            else cout<<ds.weight(y) - ds.weight(x)<<endl;
        }
    }
}