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 <algorithm>
#include <vector>

//float inf = std::numeric_limits<float>::infinity();
#define INF 100000000

using namespace std;

typedef struct UnionFind_ {
  vector<int> p;
  vector<int> r;
  vector<int> diff_weight;

  UnionFind_(int n = 1){
    init(n);
  }

  void init(int n = 1){
    p.resize(n);
    r.resize(n);
    diff_weight.resize(n);
    for(int i = 0; i < n; ++i){
      p[i] = i;
      r[i] = 0;
      diff_weight[i] = 0;
    }
  }

  int findSet(int x){
    int tmp;
    if(x != p[x]){
      tmp = findSet(p[x]);
      diff_weight[x] += diff_weight[p[x]];
      p[x] = tmp;
    }
    return p[x];
  }

  bool issame(int x, int y){
    return findSet(x) == findSet(y);
  }

  int weight(int x){
    findSet(x);
    return diff_weight[x];
  }

  int diff(int x, int y){
    if(!issame(x, y)) return INF;
    return weight(y) - weight(x);
  }

  bool merge(int x, int y, int w){
    w += weight(x);
    w -= weight(y);

    x = findSet(x);
    y = findSet(y);
    if(x == y) return false;

    if(r[x] < r[y]){
      swap(x, y);
      w = -w;
    }

    if(r[x] == r[y]) ++r[x];
    p[y] = x;


    diff_weight[y] = w;

    return true;
  }

} UnionFind;


int main(){
  int n, q;
  int com, x, y, z;
  int count = 0;

  cin >> n >> q;
  UnionFind uf(n);
  int judge[q];


  for(int i = 0; i < q; ++i){
    cin >> com;
    if(com == 0){
    cin >> x >> y >> z;
    uf.merge(x, y, z);
    }

    else{
      cin >> x >> y;
      judge[count++] = uf.diff(x, y);
    }
  }

  for(int i = 0; i < count; ++i){
    if(judge[i] >= INF) cout << "?" << endl;
    else cout << judge[i] << endl;
  }


  return 0;
}