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>
#include <algorithm>

typedef long long LL;

const int N = 1e5 + 1;

int pa[N];
LL v[N];

void init() {
  for (int i = 0; i < N; ++i) {
    pa[i] = i;
    v[i] = 0;
  }
}

int find(int x) {
  if (x != pa[x]) {
    int p = pa[x];
    pa[x] = find(pa[x]);
    v[x] += v[p];
  }
  return pa[x];
}

void unite(int x, int y, int z) {
  int px = find(x);
  int py = find(y);
  if (px != py) {
    pa[px] = py;
    v[px] = v[y] - v[x] + z;
  }
}

bool check(int x, int y) {
  int px = find(x);
  int py = find(y);
  return px == py;
}

int main() {
  int n, q;
  while (std::cin >> n >> q) {
    init();
    while (q --) {
      int op;
      std::cin >> op;
      if (op == 0) {
        int x, y, z;
        std::cin >> x >> y >> z;
        unite(x, y, z);
      } else {
        int x, y;
        std::cin >> x >> y;
        if (check(x, y)) {
          std::cout << v[x] - v[y] << std::endl;
        } else {
          std::cout << "?" << std::endl;
        }
      }
    }
  }
  return 0;
}