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 LF '\n'
#define ALL(x) x.begin(), x.end()
#define iostreamBooster() { cin.tie(nullptr); ios_base::sync_with_stdio(false); }
using namespace std;
typedef int64_t i64;
typedef pair<int,int> pii;
template<class A, class B>inline bool chmax(A &a, const B &b){return b>a ? a=b,1 : 0;}
template<class A, class B>inline bool chmin(A &a, const B &b){return b<a ? a=b,1 : 0;}
constexpr int INF = 0x3f3f3f3f;
template<class Itr> void dump(Itr begin, Itr end) { for (;begin != end; ++begin) clog << *begin << LF; }

template<class Abel>
struct WeightedUnionFind {
  vector<int> uni;
  vector<Abel> dw;

  explicit WeightedUnionFind(int n, const Abel &UNIT = 0)
    : uni(n+5, -1), dw(n+5, UNIT) {}

  int   size(int x)       { return -uni[root(x)]; }
  Abel  weight(int x)     { root(x); return dw[x]; }
  bool  same(int x, int y){ return root(x) == root(y); }
  Abel  diff(int x, int y){ return weight(y) - weight(x); }

  int root(int x) {
    if (uni[x] < 0) return x;
    const int rt = root(uni[x]);
    dw[x] += dw[uni[x]];
    return uni[x] = rt;
  }

  bool unite(int x, int y, Abel w) {
    w += weight(x) - weight(y);
    x = root(x); y = root(y);
    if (x == y) return false;
    if (uni[y] < uni[x]) swap(x,y), w = -w;
    uni[x] += uni[y]; uni[y] = x; dw[y] = w;
    return true;
  }
};

signed main()
{
  iostreamBooster();
  int n, q;
  cin >> n >> q;
  WeightedUnionFind<i64> wuf(n);

  while(q--) {
    int com, x, y, z;

    cin >> com;
    if (com == 0) {
      cin >> x >> y >> z;
      wuf.unite(x, y, z);
    } else {
      cin >> x >> y;
      if (wuf.same(x, y))
        cout << wuf.diff(x, y) << LF;
      else {
        cout << '?' << LF;
      }
    }
  }
  return 0;
}