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>
#define For(i, a, b) for(int (i)=(a); (i)<(b); (i)++)
#define rFor(i, a, b) for(int (i)=(a)-1; (i)>=(b); (i)--)
#define rep(i, n) For((i), 0, (n))
#define rrep(i, n) rFor((i), (n), 0)
using namespace std;

template<class type> struct WeightedUnionFind{
  vector<int> par;
  vector<int> treerank;
  vector<type> wdiff;
  
  WeightedUnionFind(int n){
    par.resize(n); treerank.resize(n); wdiff.resize(n);
    rep(i, n) par[i] = i, treerank[i] = 0, wdiff[i] = 0;
  }
  
  int find(int x){
    if(par[x] == x) return x;
    int r = find(par[x]);
    wdiff[x] += wdiff[par[x]];
    return par[x] = r;
  }
  
  type weight(int x){
    find(x);
    return wdiff[x];
  }
  
  void unite(int x, int y, type w){
    w += weight(x); w -= weight(y);
    x = find(x); y = find(y);
    if(x == y) return;
    if(treerank[x] < treerank[y]) swap(x, y), w = -w;
    if(treerank[x] == treerank[y]) treerank[x]++;
    par[y] = x;
    wdiff[y] = w;
    return;
  }
  
  type diff(int x, int y){
    return weight(y) - weight(x);
  }
  
  bool same(int x, int y){
    return find(x) == find(y);
  }
};

int main(){
    int n, q; cin >> n >> q;
    WeightedUnionFind<int> uf(n);
    rep(i, q){
        int c; cin >> c;;
        if(c){
            int x, y; cin >> x >> y;
            if(!uf.same(x, y)) cout << '?' << endl;
            else cout << uf.diff(x, y) << endl;
        }
        else{
            int x, y, z; cin >> x >> y >> z;
            uf.unite(x, y, z);
        }
    }
}