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 <bits/stdc++.h>
using namespace std;
class disjoint_set {
  public:
  vector<int> rank, prt, ptl;
  disjoint_set (int size) {
    rank.resize(size);
    prt.resize(size);
    ptl.resize(size);
    for (int i = 0; i < size; i++) {
      prt[i] = i;
      rank[i] = 0;
      ptl[i] = 0;
    }
  }
  int find (int x) {
    if (x == prt[x]){
      return x;
    } else {
      int r = find(prt[x]);
      ptl[x] += ptl[prt[x]];
      return prt[x] = r;
    }
  }
  bool is_equiv (int x, int y) {
    return find(x) == find(y);
  }
  bool unite (int x, int y, int w) {
    if (find(x) == find(y)) {
      return false;
    }
    w += ptl[x];
    w -= ptl[y];
    x = find(x);
    y = find(y);
    if (rank[x] < rank[y]) {
      swap(x, y);
      w *= -1;
    }
    prt[y] = x;
    ptl[y] = w;
    if (rank[x] == rank[y]) {
      rank[x]++;
    }
    return true;
  }
  int diff (int x, int y) {
    find(x);
    find(y);
    return ptl[y] - ptl[x];
  }
};
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, q;
  cin >> n >> q;
  disjoint_set djs(n);
  while (q--) {
    int c;
    cin >> c;
    if (c == 0) {
      int x, y, z;
      cin >> x >> y >> z;
      djs.unite(x, y, z);
    } else {
      int x, y;
      cin >> x >> y;
      if (!djs.is_equiv(x, y)) {
        cout << "?" << '\n';
      } else {
        cout << djs.diff(x, y) << '\n';
      }
    }
  }
  return 0;
}