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 <algorithm>
#include <stdio.h>
#include <vector> 
#include <math.h>
using namespace std;

vector<int> Parent;
vector<int> Rank;
vector<int> DiffW;

int findSet(int x);

int getWeight(int x){
  findSet(x);
  return DiffW[x];
}

int diffWeight(int x, int y){
  return getWeight(y) - getWeight(x);
}

void makeSet(int x){
  Parent.push_back(x);
  Rank.push_back(0);
  DiffW.push_back(0);
}
int findSet(int x){
  if( x != Parent[x] ){
    int r = findSet(Parent[x]);
    DiffW[x] += DiffW[Parent[x]];
    Parent[x] = r;
  }
  return Parent[x];
}
void link(int x, int y, int w){
  if( Rank[x] > Rank[y] ){
    Parent[y] = x;
    DiffW[y] = w;
  }else{
    Parent[x] = y;
    DiffW[x] = -w;
    if( Rank[x] == Rank[y] ){
      Rank[y] = Rank[y] + 1;
    }
  }
}

void unite(int x, int y, int w){
  w += getWeight(x); w-= getWeight(y);  
  link(findSet(x), findSet(y), w);
}

int same(int x, int y){
  if(findSet(x)==findSet(y)){
    return 1;
  }
  return 0;
}

int main(){
  int n, q;
  scanf("%d %d" ,&n ,&q);
  for( int i = 0 ; i < n ; i++ ){
    makeSet(i);
  }
  for( int i = 0 ; i < q ; i++ ){
    int com, x, y, z;
    scanf("%d" ,&com);
    if(com == 0){ // 0(relate) x y z
      scanf("%d %d %d" ,&x ,&y ,&z);
      unite(x, y, z);
    }else{ // 1(diff) x y
      scanf("%d %d" ,&x ,&y);
      if(same(x,y)){
        int di = diffWeight(x, y);
        printf("%d\n" ,di );
      }else{
        printf("?\n");
      }
    }
  }

  return 0;
}