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>
using namespace std;

#define MAX 100000
#define INF 1 << 31

struct Node 
{
  int parent;
  int cost;
};

int parent[MAX];
int depth[MAX];
int cost[MAX];

Node findParent(int child)
{
  Node tmp;
  if (child != parent[child])
  {
    tmp = findParent(parent[child]);
    parent[child] = tmp.parent;
    cost[child] += tmp.cost;
  }

  tmp.parent = parent[child];
  tmp.cost = cost[child];

  return tmp;
}

void relate(int x, int y, int z)
{
  Node nodeX = findParent(x);
  Node nodeY = findParent(y);

  if (nodeX.parent == nodeY.parent) return;

  if (depth[nodeY.parent] > depth[nodeX.parent])
  {
    parent[nodeX.parent] = nodeY.parent;
    cost[nodeX.parent] = nodeY.cost - nodeX.cost - z;
  }
  else
  {
    parent[nodeY.parent] = nodeX.parent;
    cost[nodeY.parent] = nodeX.cost - nodeY.cost + z;

    if (depth[nodeX.parent] == depth[nodeY.parent])
    {
      depth[nodeX.parent]++;
    }
  }
}

int diff(int x, int y)
{
  Node NodeX = findParent(x);
  Node NodeY = findParent(y);

  if (NodeX.parent != NodeY.parent) return INF;

  return NodeY.cost - NodeX.cost;
}

int main()
{
  int n, q, i, query, x, y, z, ans;

  cin >> n >> q;
  for (i = 0; i < n; i++) 
  {
    parent[i] = i;
    depth[i] = 0;
    cost[i] = 0;
  }

  for (i = 0; i < q; i++)
  {
    cin >> query;
    if (query == 0) 
    {
      cin >> x >> y >> z;
      relate(x, y, z);
    }
    else 
    {
      cin >> x >> y;
      ans = diff(x, y);
      if (ans == INF) cout << "?" << endl;
      else cout << ans << endl;
    }
  }

  return 0;
}