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 <algorithm>
#include <iostream>
#include <vector>
using namespace std;

template<typename T>
struct WeightedUnionFind {
    vector<int> data;
    vector<T> ws;
    WeightedUnionFind(int sz) : data(sz, -1), ws(sz) { }
    bool merge(int x, int y, T w) {             // ws(y) = ws(x) + w
        w += weight(x); w -= weight(y);
        if ((x = root(x)) == (y = root(y))) return false;
        if (data[x] > data[y]) swap(x, y), w = -w;
        data[x] += data[y]; data[y] = x; ws[y] = w;
        return true;
    }
    bool find(int x, int y) { return root(x) == root(y); }
    T diff(int x, int y) { return weight(y) - weight(x); }
    T weight(int t) { root(t); return ws[t]; }
    int root(int k) {
        if (data[k] < 0) return k;
        int par = root(data[k]);
        ws[k] += ws[data[k]];
        return data[k] = par;
    }
};

int main() {
    int n, q; cin >> n >> q;
    WeightedUnionFind<int> wuf(n);
    while (q--) {
        int com, x, y; cin >> com >> x >> y;
        if (com == 0) {
            int z; cin >> z;
            wuf.merge(x, y, z);
        } else {
            if (wuf.find(x, y)) {
                cout << wuf.diff(x, y) << endl;
            } else {
                cout << "?" << endl;
            }
        }
    }
    return 0;
}