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 namespace std;

template<class T> struct WeightedUnionFind {
    int sz;
    vector<int> data;
    vector<T> potential;

    WeightedUnionFind (int sz, T id = 0)
        : sz(sz), data(sz, -1), potential(sz, id) { }

    // potential[y] = potential[x] + w
    bool unite (int x, int y, T w) {
        w += (weight(x) - weight(y));
        x = root(x); y = root(y);
        if (x == y) return false;
        if (data[x] > data[y]) { swap(x, y); w = -w; }
        data[x] += data[y];
        data[y] = x;
        potential[y]= w;
        sz--;
        return true;
    }

    bool is_same (int x, int y) { return root(x) == root(y); }

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

    T weight (int x) { root(x); return potential[x]; }

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

    size_t size () { return (size_t)sz; }

    size_t size (int x) { return (size_t)-data[root(x)]; }

};



int main() {
    int n, q;
    cin >> n >> q;
    WeightedUnionFind<int> uf(n);
    
    while (q--) {
        int t;
        cin >> t;
        if (t == 0) {
            int x, y, w;
            cin >> x >> y >> w;
            uf.unite(y, x, w);
        } else {
            int x, y;
            cin >> x >> y;
            if (uf.is_same(x, y)) {
                cout << uf.diff(y, x) << '\n';
            } else {
                cout << '?' << '\n';
            }
        }
    }
    return 0;
}