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 <vector>
#include <cassert>

template<class T>
struct potentialized_union_find {
    using value_type = T;
    using size_type = std::size_t;
private :
    size_type _size;
    std::vector<int> node;
    std::vector<value_type> potential;

public :
    potentialized_union_find (size_type n, const value_type &ie) : 
        _size(n), node(n, -1), potential(n, ie) { }

    size_type root (size_type x) {
        if (node[x] < 0) return x;
        int r = root(node[x]);
        potential[x] += potential[node[x]];
        return (node[x] = r);
    }

    value_type weight (size_type x) {
        root(x);
        return (potential[x]);
    }

    bool unite (size_type x, size_type y, value_type p) {
        p += (weight(x) - weight(y));
        if ((x = root(x)) == (y = root(y))) return false;
        if (node[x] > node[y]) {
            std::swap(x, y);
            p = -p;
        }
        node[x] += node[y];
        node[y] = x;
        potential[y] = p;
        _size--;
        return true;
    }

    bool same (size_type x, size_type y) {
        return (root(x) == root(y));
    }

    value_type diff (size_type x, size_type y) {
        assert(same(x, y));
        return (weight(y) - weight(x));
    }

    const size_type& size () const noexcept {
        return (_size);
    }

    size_type size (size_type x) {
        return (size_type(-node[root(x)]));
    }

};


#include <iostream>

int main() {
    std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);

    std::size_t n;
    int query;
    std::cin >> n >> query;

    potentialized_union_find<int> uf(n, 0);

    while (query--) {
        int type;
        std::cin >> type;
        if (type == 0) {
            std::size_t x, y;
            int p;
            std::cin >> x >> y >> p;
            uf.unite(x, y, p);
        } else {
            std::size_t x, y;
            std::cin >> x >> y;
            if (uf.same(x, y)) {
                std::cout << uf.diff(x,y) << '\n';
            } else {
                std::cout << '?' << '\n';
            }
        }
    }

    return 0;
}