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 ll = long long;
using namespace std;

const int inf = 1e9;
const ll linf = 1e18;

template<typename T = int>
class WeightedUnionFind
{
public:
    WeightedUnionFind(int n = 0, T unity = 0) : m_data(n, -1), m_weight(n, unity), m_count(n) {}

    int find(int x)
    {
        if (m_data[x] < 0) return x;

        int root = find(m_data[x]);
        m_weight[x] += m_weight[m_data[x]];
        return m_data[x] = root;
    }

    T weight(int x)
    {
        find(x);
        return m_weight[x];
    }

    bool unite(int x, int y, T w)
    {
        w += weight(x), w -= weight(y);
        x = find(x), y = find(y);
        if (x == y) return false;

        if (m_data[x] > m_data[y]) {
            swap(x, y);
            w = -w;
        }
        m_data[x] += m_data[y];
        m_data[y] = x;
        m_weight[y] = w;
        m_count--;
        return true;
    }

    bool same(int x, int y) { return find(x) == find(y); }

    T diff(int x, int y) { return weight(y) - weight(x); }

    int size(int x) { return -m_data[find(x)]; }

    int count(void) const { return m_count; }

private:
    vector<int> m_data;
    vector<T>   m_weight;
    int m_count; 
};

int main()
{
    int n, q; cin >> n >> q;
    WeightedUnionFind<int> uf(n);
    for (int i = 0; i < q; i++) {
        int p; cin >> p;
        if (!p) {
            int x, y, z; cin >> x >> y >> z;
            uf.unite(x, y, z);
        } else {
            int x, y; cin >> x >> y;
            if (uf.same(x, y)) cout << uf.diff(x, y) << endl;
            else cout << "?" << endl;
        }
    }
    return 0;
}