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;

#define rep(i,n) for(i = 0;i < n;++i)
#define all(v) v.begin(), v.end()
using ll = long long;

struct UFweight
{
    int i;
    vector<int> par;
    vector<int> size;
    vector<int> rank;
    vector<ll> diff_weight;
    UFweight(int n, ll sum_unity = 0){
        par.resize(n);  rank.resize(n); size.resize(n); diff_weight.resize(n);
        for(i = 0;i < n;++i){
            par.at(i) = i;
            rank.at(i) = 0;
            size.at(i) = 1;
            diff_weight.at(i) = sum_unity;
        }
    }
    
    int root(int x){
        if(par.at(x) == x){
            return x;
        }else{
            int r = root(par.at(x));
            diff_weight.at(x) += diff_weight.at(par.at(x));
            return par.at(x) = r;
        }
    }
    
    ll weight(int x){
        root(x);
        return diff_weight.at(x);
    }
    
    ll get_diff(int x, int y){
        return weight(y) - weight(x);
    }
    
    // weight(y) - weight(x) = wとなるようにmerge
    bool merge(int x, int y, ll w){
        w += weight(x); w -= weight(y);
        int rx = root(x);
        int ry = root(y);
        if(rx == ry){
            ll weight_diff = get_diff(rx, ry);
            if(weight_diff == w) return true;
            else return false;
        }
        
        if(rank.at(rx) < rank.at(ry)){
            swap(rx,ry);
            w *= -1;
        }
        if(rank.at(rx) == rank.at(ry)) ++rank.at(rx);
        par.at(ry) = rx;
        diff_weight.at(ry) = w;
        size.at(rx) += size.at(ry);
        
        return true;
    }
    
    bool same(int x, int y){
        int rx = root(x);
        int ry = root(y);
        return rx == ry;
    }
    
    int get_size(int x){
        return size.at(root(x));
    }
};

int main()
{
    ll i,j;
    ll n,q;
    cin >> n >> q;
    UFweight uf(n);
    for(i = 0;i < q;++i){
        ll com;
        cin >> com;
        if(com == 0){
            ll x,y,z;
            cin >> x >> y >> z;
            uf.merge(x, y, z);
        }else{
            ll x, y;
            cin >> x >> y;
            if(uf.same(x, y)){
                cout << uf.get_diff(x, y) << endl;
            }else{
                cout << '?' << endl;
            }
        }
    }

    return 0;
}