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>
#include <algorithm>

struct Weighted_Union_Find {
    std::vector<int> par;
    std::vector<int> rank;
    std::vector<long long> wdiff;
    //初期化
    void init( int n ) {
        par.resize( n );
        rank.resize( n );
        wdiff.resize( n );
        for ( int i = 0; i < n; ++i ) {
            par[ i ] = i;
            rank[ i ] = 0;
            wdiff[ i ] = 0;
        }
    }
    
    //木の根を探す
    int find( int s ) {
        if ( par[ s ] == s ) {
            return s;
        }
        int r = find(par[ s ]);
        wdiff[s] += wdiff[par[s]];
        return par[s] = r;
    }
    
    long long weight(int x) {
        find(x); // 経路圧縮
        return wdiff[x];
    }

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

    //結合
    bool unite( int x, int y, long long w ) {
        w += weight(x);
        w -= weight(y);
        x = find( x );
        y = find( y );
        if ( x == y ) {
            return false;
        }
        if ( rank[ x ] < rank[ y ] ) {
            std::swap(x, y);
            w = -w;
        }
        if ( rank[x] == rank[y] ) ++rank[x];
        par[y] = x;
        wdiff[y] = w;
        return true;
    }
    
    //二つの数の根が同じかどうか
    bool same( int x, int y ) {
        return find( x ) == find( y );
    }
    
    //サイズを返す
    unsigned int size() {
        return par.size();
    }
};

using namespace std;

int main(){
    int n, q;
    cin >> n >> q;
    Weighted_Union_Find wuf;
    wuf.init(n);
    while(q--){
        int query;
        cin >> query;
        if(query){
            int x, y;
            cin >> x >> y;
            if(!wuf.same(x, y)){
                cout << "?\n";
            }else{
                cout << wuf.diff(x, y) << "\n";
            }
        }else{
            int x, y, z;
            cin >> x >> y >> z;
            wuf.unite(x, y, z);
        }
    }
}