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;

class UnionFind {

public:
    vector<int> par;
    vector<int> rank;
    vector<int> relative_diff;
    
    UnionFind( int n ) {
	par.resize( n );
	rank.resize( n );
	relative_diff.resize( n );
	for ( int i=0; i<n; ++i ) par[i] = i;
    }

    int Root( int x ) {

	if ( x == par[x] ) return x;

	int r = Root( par[x] );
	relative_diff[x] += relative_diff[par[x]];
	par[x] = r;
	return r;
    }
    
    bool IsSame( int x, int y ) {
	return Root( x ) == Root( y );
    }

    void Merge( int x, int y, int w ) {

	w += TotalDiff( x );
	w -= TotalDiff( y );	
	
	x = Root( x );
	y = Root( y );

	if ( x == y ) return;

	if ( rank[x] < rank[y] ) {//yの方が深い
	    relative_diff[x] = -w;
	    par[x] = y;//xをyのグループのルートにつなぐ
	}
	else {//xの方が深いか 同じ深さ
	    relative_diff[y] = w;
	    par[y] = x;//yをxのグループのルートにつなぐ
	    if ( rank[x] == rank[y] ) ++rank[x];
	}
	
    }

    int TotalDiff( int x ) {
	Root( x );
	return relative_diff[x];
    }
    
    int Diff( int x, int y ) {
	return TotalDiff( y ) - TotalDiff( x );
    }
};

int main() {

    int n, l;
    cin >> n >> l;
    
    UnionFind un(n);

    for ( int i=0; i<l; ++i ) {
	int type, a, b;
	cin >> type >> a >> b;
	if ( type == 0 ) {
	    int w;
	    cin >> w;
	    un.Merge( a, b, w );
	}
	else {
	    if ( un.IsSame( a, b ) )
		cout << un.Diff( a, b ) << endl;
	    else
		cout << "?" << endl;
	}
    }

    
    return 0;
}