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>
using namespace std;

#define SIZE 100000

int main(void)
{
    int n, q;
    int com, x, y, z;
    int rootX, rootY;
    int diffX, diffY;
    int parent[SIZE + 1];
    int parent_diff[SIZE + 1] = {};
    
    cin >> n >> q;
    
    for(int i = 0; i <= n; ++i)
    {
        parent[i] = i;
    }
    
    for(int i = 0; i < q; ++i)
    {
        cin >> com;
        
        if(com == 0)
        {
            cin >> x >> y >> z;
            
            diffX = 0;
            rootX = x;
            while(parent[rootX] != rootX)
            {
                diffX += parent_diff[rootX];
                rootX = parent[rootX];
            }
            diffY = 0;
            rootY = y;
            while(parent[rootY] != rootY)
            {
                diffY += parent_diff[rootY];
                rootY = parent[rootY];
            }
                
            if(rootX < rootY)
            {
                parent[rootY] = rootX;
                parent_diff[rootY] = diffX - diffY - z;
            }
            else
            {
                parent[rootX] = rootY;
                parent_diff[rootX] = diffY - diffX + z;
            }
        }
        else if(com == 1)
        {
            cin >> x >> y;
            
            diffX = 0;
            rootX = x;
            while(parent[rootX] != rootX)
            {
                diffX += parent_diff[rootX];
                rootX = parent[rootX];
            }
            diffY = 0;
            rootY = y;
            while(parent[rootY] != rootY)
            {
                diffY += parent_diff[rootY];
                rootY = parent[rootY];
            }
            
            if(rootX == rootY)
                cout << diffX - diffY << endl;
            else
                cout << '?' << endl;
        }
    }
    
    return 0;
}