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;

const int N=1e5+10;
int p[N],dst[N];

void init(int n)
{
    for(int i=0;i<=n;i++) p[i]=i,dst[i]=0;
}

int fnd(int x)
{
    if(p[x]!=x)
    {
        int tmp=fnd(p[x]);
        dst[x]+=dst[p[x]];
        return p[x]=tmp;
    }else
    {
        dst[x]=0;
        return x;
    }
}

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

bool unite(int x,int y,int z)
{
    if(same(x,y)) return false;

    int px=fnd(x),py=fnd(y);

    p[px]=py;
    dst[px]=dst[y]-z-dst[x];

    return true;
}

int dif(int x,int y)
{
    fnd(x),fnd(y);

    return dst[y]-dst[x];
}

int main()
{
    int n,q;
    cin>>n>>q;

    init(n);

    while(q--)
    {
        int op,x,y;
        cin>>op>>x>>y;

        if(!op)
        {
            int z;
            cin>>z;

            unite(x,y,z);
        }else
        {
            if(same(x,y))
                cout<<dif(x,y)<<endl;
            else
                cout<<"?"<<endl;
        }
    }

    return 0;
}