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 <cassert>
#include <iostream>
#include <vector>

//
// 重み付きUnion-Find Tree size version
//
// verify: AOJ DSL_1_B
//
template <typename T>
struct WeightedUnionFind {
    std::vector<int> data;
    std::vector<T> ws;
    const int n;
    WeightedUnionFind(int num) : data(num, -1), ws(num), n(num) {}
    int find(int k) {
        assert(0 <= k && k < n);
        if (data[k] < 0) return k;
        auto par = find(data[k]);
        ws[k] += ws[data[k]];
        return data[k] = par;
    }
    T weight(int k) {
        assert(0 <= k && k < n);
        find(k);
        return ws[k];
    }
    bool unite(int x, int y, T w) {
        assert(0 <= x && x < n);
        assert(0 <= y && y < n);
        w += weight(x);
        w -= weight(y);
        x = find(x);
        y = find(y);
        if (x == y) return false;
        if (data[x] > data[y]) {
            std::swap(x, y);
            w *= -1;
        }
        data[x] += data[y];
        data[y] = x;
        ws[y] = w;
        return true;
    }
    int size(int k) {
        assert(0 <= k && k < n);
        return (-data[find(k)]);
    }
    T diff(int x, int y) {
        assert(0 <= x && x < n);
        assert(0 <= y && y < n);
        return weight(y) - weight(x);
    }
};

int main() {
    int N, M;
    std::cin >> N >> M;
    WeightedUnionFind<int> uf(N);
    while (M--) {
        int a, b, c, d;
        std::cin >> a >> b >> c;
        if (a == 0) {
            std::cin >> d;
            uf.unite(b, c, d);
        } else {
            if (uf.find(b) == uf.find(c)) {
                std::cout << uf.diff(b, c) << std::endl;
            } else {
                std::cout << "?" << std::endl;
            }
        }
    }
    return 0;
}