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;
using ll = long long;

template<typename T> struct UnionFind {
  vector<int> par;
  vector<int> rank;
  vector<T> ws;

  UnionFind(int n = 1, T e = 0)
      : par(n), rank(n), ws(n) {
    init(n, e);
  }

  void init(int n, T e) {
    for (int i = 0; i < n; ++i) {
      par[i] = i;
      rank[i] = 0;
      ws[i] = e;
    }
  }
  int root(int x) {
    if (par[x] == x) {
      return x;
    } else {
      int r = root(par[x]);
      ws[x] += ws[par[x]];
      return par[x] = r;
    }
  }
  bool same(int x, int y) {
    return root(x) == root(y);
  }
  T weight(int x) {
    root(x);
    return ws[x];
  }
  T diff(int x, int y) {
    return weight(y) - weight(x);
  }
  bool unite(int x, int y, T w = 0) {
    w -= weight(y) - weight(x);
    x = root(x);
    y = root(y);
    if (x == y) return false;

    if (rank[x] < rank[y]) {
      swap(x, y);
      w = negate<T>()(w);
    }
    par[y] = x;
    ws[y] = w;
    if (rank[x] == rank[y]) ++rank[x];
    return true;
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int n, q; cin >> n >> q;
  UnionFind<ll> uf(n);

  while (q--) {
    int com; cin >> com;
    if (com) {
      int x, y; cin >> x >> y;
      cout << ( (uf.same(x, y)) ? to_string(uf.diff(x, y)) : "?" ) << endl;
    } else {
      int x, y, z; cin >> x >> y >> z;
      uf.unite(x, y, z);
    }
  }
  return 0;
}