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>

using namespace std;

int par[100000];
int weight_diff[100000];

void init(int n){
  for(int i=0; i<n; i++) par[i] = i;
}
 
int root(int x){
  if(par[x] == x){
    return x;
  }else{
    int n = root(par[x]);
    weight_diff[x] += weight_diff[par[x]];
    return par[x] = n;
  }
}

int weight(int x) {
  root(x);
  return weight_diff[x];
}

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

bool same(int x, int y){
  return root(x) == root(y);
}
	
void unite(int x, int y, int w){
  w += weight(x); w -= weight(y);
  x = root(x);
  y = root(y);
  if(x == y) return;
  weight_diff[y] = w;
  par[y] = x;
}

int main()
{
  int n,q;
  cin >> n >> q;
  int p, a, b, w;
  init(n);
  for(int i=0; i<q; i++){
    cin >> p;
    if(p == 0){
      cin >> a >> b >> w;
      unite(a, b, w);
    }
    else{
      cin >> a >> b;
      cout << (same(a, b) ? to_string(diff(a,b)) : "?") << endl;
    }
  }
  
  return 0;
}