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,a) for(int i = 0; i < (a); i++)
#define ALL(a) (a).begin(),(a).end()
typedef long long ll;
typedef pair<int, int> P;
const int INF = 1e9;
const long long LINF = 1e18;
const long long MOD = 1e9 + 7;

template <typename T>
struct WeightedUnionFind{
    vector<int> par,siz;
    vector<T> ws;

    WeightedUnionFind(int n) : par(n), siz(n, 1), ws(n, T(0)){
        iota(par.begin(), par.end(), 0);
    }

    int root(int x){
        if(par[x] == x) return x;
        int t = root(par[x]);
        ws[x] += ws[par[x]];
        return par[x] = t;
    }

    T weight(int x){
        root(x);
        return ws[x];
    }

    void unite(int x, int y, T w){
        w += weight(x);
        w -= weight(y);
        x = root(x);
        y = root(y);
        if(x == y) return;
        if(siz[x] < siz[y]){
            swap(x, y);
            w = -w;
        }
        siz[x] += siz[y];
        par[y] = x;
        ws[y] = w;
    }

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

    int size(int x){
        return siz[root(x)];
    }

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

signed main(){
    int n,Q;
    cin >> n >> Q;
    WeightedUnionFind<int> wuf(n);
    while(Q--){
        int q;
        cin >> q;
        int x,y,z;
        if(q == 0){
            cin >> x >> y >> z;
            wuf.unite(x, y, z);
        }else{
            cin >> x >> y;
            if(!wuf.same(x, y)) cout << "?" << endl;
            else cout << wuf.diff(x, y) << endl;
        }
    }
    return 0;
}