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;
#define rep(i,n) for(int i=0;i<(n);i++)

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> P;

#define MAX 100005
#define INF 1001001001

int n;
vector<int> par, ranks, weight;

void init(int n) {
  ranks.assign(n,0);
  weight.assign(n,0);
  par.resize(n);
  iota(par.begin(), par.end(), 0);
}

int root(int x) {
  if (par[x] == x) return x;
  int rx = root(par[x]);
  weight[x] += weight[par[x]];
  return par[x] = rx;
}

bool isSame(int x, int y) {
  return root(x) == root(y);
}

int getWeight(int x) {
  root(x); // 経路圧縮
  return weight[x];
}

int getDiff(int x, int y) {
  return getWeight(y) - getWeight(x);
}

bool merge(int x, int y, int w) {
  int rx = root(x);
  int ry = root(y);
  if (rx == ry) return false;

  int rw = w;
  rw += getWeight(x);
  rw -= getWeight(y);

  if (ranks[rx] < ranks[ry]) swap(rx,ry), rw = -rw;
  par[ry] = rx;
  weight[ry] = rw;
  if (ranks[rx] == ranks[ry]) ranks[rx]++;

  return true;
}

int main(int, char**)
{
  cin >> n;
  init(n);

  int q; cin >> q;
  vector<int> ans;
  rep(i,q) {
    int command;
    cin >> command;
    if (command == 0) {
      int x, y, z;
      cin >> x >> y >> z;
      merge(x,y,z);
    } else {
      int x, y;
      cin >> x >> y;
      if (isSame(x,y)) ans.push_back(getDiff(x,y));
      else ans.push_back(INF);
    }
  }
  for (auto a : ans) 
    if (a!=INF) cout << a << endl;
    else cout << "?" << endl;

  return 0;
}