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 <sstream>
#include <cstdio>
#include <stdlib.h>
#include <string>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
#define MAX 100002

int p[MAX];
int diff_w[MAX];
int r[MAX];

int root(int x){
    if(p[x]==x)return x;
    int r = root(p[x]);
    diff_w[x] += diff_w[p[x]];
    return p[x] = r;
}

void diff(int x,int y){
  if(root(x)==root(y))cout<<diff_w[y] - diff_w[x]<<endl;
  else cout<<"?"<<endl;
}
bool same(int x,int y){
  return root(x)==root(y);
}
void Union(int x,int y){
  p[x]=y;
}

void merge(int x,int y,int w){
  int rx = root(x);
  int ry = root(y);
  w = w + diff_w[x] - diff_w[y];
  if(r[rx]<r[ry]) {
    swap(rx,ry);
    w = -w;
  }
  r[rx]+=r[ry];
  p[ry] = rx;
  diff_w[ry] = w;
  //cout<<"w:"<<w<<endl;
}

int main(){
  int n,q,x,y,z,rx,ry,flag;
  cin>>n>>q;
  for(int i=0;i<n+1;i++){
    p[i] = i;
    r[i] = 1;
  }
  for(int i=0;i<q;i++){
    cin>>flag>>x>>y;
    if(flag==1){
      diff(x,y);
    }
    else{
      cin>>z;
      merge(x,y,z);
    }
  }
  //for(int i=0;i<n+1;i++)cout<<i<<" root:"<<p[i]<<" diff_w:"<<diff_w[i]<<" rank:"<<r[i]<<endl;
  return 0;
}