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;

template <class T>
struct Unionfindw {
  // tree number
  vector<int> par;
  // tree rank
  vector<int> treerank;
  // edge weight
  vector<T> weight;
  const int inf = 2147483647;
  // constructor
  Unionfindw(int n = 1, T initialnum = 0) {
    stree(n + 1, initialnum);
  }
  // make and initialization
  void stree(int n = 1, T initialnum = 0) {
    par.assign(n, -1);
    treerank.assign(n, 0);
    weight.assign(n, initialnum);
  }
  // search root
  int root(int x) {
    if(par[x] < 0) return x;
    int rx = root(par[x]);
    weight[x] += weight[par[x]];
    return par[x] = rx;
  }
  // is same?
  bool issame(int x, int y) { return root(x) == root(y); }
  // calculate weight
  T calcw(int x) {
    root(x);
    return weight[x];
  }
  // add
  // x+w = y
  // already added, return 0
  bool uni(int x, int y, T w = 0) {
    w += calcw(x);
    w -= calcw(y);
    x = root(x);
    y = root(y);
    if(x == y) return 0;
    if(treerank[x] > treerank[y]) swap(x, y);
    if(treerank[x] == treerank[y]) ++treerank[x];
    par[y] -= size(x);
    par[x] = y;
    weight[x] = -w;
    return 1;
  }

  int size(int x) { return -par[root(x)]; }

  // calculate difference between x and y (y-x)
  // if not same tree, return 1
  T calcdiff(int x, int y) {
    if(!issame(x, y)) return inf;
    return calcw(y) - calcw(x);
  }
};

long long n, q;

int main() {
  cin >> n >> q;
  Unionfindw<long long> uf(n);
  for(int i = 0; i < q; ++i) {
    long long c, x, y, z;
    cin >> c >> x >> y;
    if(c) {
      z = uf.calcdiff(x, y);
      if(z == uf.inf)
        cout << "?" << endl;
      else
        cout << z << endl;
    }
    else {
      cin >> z;
      uf.uni(x, y, z);
    }
  }
  return 0;
}