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>
using namespace std;

template<class Abel> struct UnionFind {
    vector<int> par;
    vector<int> rank;
    vector<Abel> diff_weight;

    UnionFind(int n = 1, Abel SUM_UNITY = 0) {
        init(n, SUM_UNITY);
    }

    void init(int n = 1, Abel SUM_UNITY = 0) {
        par.resize(n); rank.resize(n); diff_weight.resize(n);
        for (int i = 0; i < n; ++i) par[i] = i, rank[i] = 0, diff_weight[i] = SUM_UNITY;
    }

    int root(int x) {
        if (par[x] == x) {
            return x;
        }
        else {
            int r = root(par[x]);
            diff_weight[x] += diff_weight[par[x]];
            return par[x] = r;
        }
    }

    Abel weight(int x) {
        root(x);
        return diff_weight[x];
    }

    bool issame(int x, int y) {
        return root(x) == root(y);
    }

    bool merge(int x, int y, Abel w) {
        w += weight(x); w -= weight(y);
        x = root(x); y = root(y);
        if (x == y) return false;
        if (rank[x] < rank[y]) swap(x, y), w = -w;
        if (rank[x] == rank[y]) ++rank[x];
        par[y] = x;
        diff_weight[y] = w;
        return true;
    }

    Abel diff(int x, int y) {
        return weight(y) - weight(x);
    }
};


int main(){
    int n,q;
    int x,y,z;
    int count=0;
    cin>>n>>q;
    UnionFind<int> U(n);
    int info;
    int diff[q];
    for(int i=0;i<q;i++){
        cin>>info;
        if(info==0){
        cin>>x>>y>>z;
        U.merge(x,y,z);
        }

        if(info==1){
        cin>>x>>y;
        if(U.issame(x,y)){
        cout<<U.diff(x, y)<<endl;
        }
        else{
            cout<<"?"<<endl;
        }
        }
    }

    return 0;
}