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"

class WeightedUnionFind {
  std::vector<int> par;  // 親の番号
  std::vector<int> ws;   // 親との重みの差

 public:
  WeightedUnionFind(int n) : par(n, -1), ws(n, 0) {}

  // x の親を返す
  int find(int x) {
    if (par[x] < 0) {
      return x;
    } else {
      int parent = find(par[x]);
      ws[x] += ws[par[x]];
      return par[x] = parent;
    }
  }

  // x の重み(親との相対値)を返す
  int weight(int x) {
    find(x);
    return ws[x];
  }

  // 頂点 x, y を (xの重み) + w = (yの重み) となるように Unite
  bool unite(int x, int y, int w) {
    w += weight(x);
    w -= weight(y);
    x = find(x);
    y = find(y);

    if (x != y) {
      if (par[y] < par[x]) {  // 多い方が根になるようにスワップする.
        int tmp = x;
        x = y;
        y = tmp;
        w = -w;
      }
      par[x] += par[y];
      par[y] = x;
      ws[y] = w;
      return true;
    } else {
      return false;
    }
  }

  bool same(int x, int y) { return find(x) == find(y); }

  void init(int size) {
    for (int i = 0; i < size; i++) {
      par[i] = -1;
      ws[i] = 0;
    }
  }
};

using namespace std;

int main() {
  int n, q;
  cin >> n >> q;
  WeightedUnionFind uf(n);
  for (int i = 0; i < q; i++) {
    int id;
    cin >> id;
    if (id) {
      int x, y;
      cin >> x >> y;
      if (uf.same(x, y)) {
        cout << -uf.weight(x) + uf.weight(y) << endl;
      } else {
        cout << "?" << endl;
      }
    } else {
      int x, y, z;
      cin >> x >> y >> z;
      uf.unite(x, y, z);
    }
  }
}