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 <vector>

using namespace std;

template<class T>
struct WeightUnionFind {
  vector<int> tree;
  vector<int> rank;
  vector<T> diff_weight;

  WeightUnionFind (int size) : tree(size, -1), rank(size, 0), diff_weight(size, 0) {} ;

  int root(int a) {
    if (tree[a] < 0) return a;
    int res = root(tree[a]);
    diff_weight[a] += diff_weight[tree[a]];
    return tree[a] = res;
  }

  bool same(int a, int b) {
    return root(a) == root(b);
  }

  bool unite(int a, int b, T w) {
    w += weight(a); w -= weight(b);
    a = root(a); b = root(b);
    if (a == b) return false;
    if (rank[a] < rank[b]) {
      swap(a, b);
      w *= -1;
    }
    if (rank[a] == rank[b]) ++rank[a];
    tree[b] = a;
    diff_weight[b] = w;
    return true;
  }

  T weight(int a) {
    root(a);
    return diff_weight[a];
  }

  T diff(int a, int b) {
    return weight(b) - weight(a);
  }
};

#define rep(i, a, n) for(int i = a; i < (n); ++i)

int main(){
  int n, m;
  cin >> n >> m;
  
  WeightUnionFind<int> wuf(n);
  rep(i, 0, m) {
    int a, b, c, d;
    cin >> a >> b >> c;
    if (a == 0) {
      cin >> d;
      wuf.unite(b, c, d);
    } else {
      if (wuf.same(b, c)) {
        cout << wuf.diff(b, c) << endl;
      } else {
        cout << "?" << endl;
      }
    }
  }
}