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;
typedef long long ll;
#define rep(i, N) for (int i = 0; i < (int)N; i++)

class UnionFindTree {
  struct edge {
    int node;
    int distance;
  };
  vector<edge> root;
  vector<int> rank;

  edge findRoot(int x) {
    if(x != root[x].node) {
      edge e = findRoot(root[x].node);
      root[x] = edge{e.node, e.distance + root[x].distance};
    }
    return root[x];
  }

public:

  UnionFindTree(int size) {
    rank = vector<int>(size, 0);
    root = vector<edge>(size, edge{});
    for(int i = 0; i < size; i++) root[i] = edge{i,0};
  }

  void relate(int x, int y, int z) {
    edge ex = findRoot(x);
    edge ey = findRoot(y);
    if(ex.node == ey.node)return;

    int d = z + ey.distance - ex.distance;
    if(rank[ex.node] < rank[ey.node]) {
      root[ex.node] = edge{ey.node, d};
    } else {
      root[ey.node] = edge{ex.node, -d};
      if(rank[ex.node] == rank[ey.node]) rank[ex.node]++;
    }
  }

  string difference(int x, int y) {
    edge ex = findRoot(x);
    edge ey = findRoot(y);
    if(ex.node == ey.node) {
      return to_string(ex.distance - ey.distance);
    } else {
      return "?";
    };
  }
};

int main () {
  int n, q;
  cin >> n >> q;
  UnionFindTree uft(n);

  rep(i,q) {
    int c, x, y, z;
    cin >> c;
    if(c == 0) {
      cin >> x >> y >> z;
      uft.relate(x, y, z);
      continue;
    }
    cin >> x >> y;
    cout << uft.difference(x, y) << endl;
  }

  return 0;
}