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 <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <deque>
#include <queue>
#include <array>
#include <set>
#include <map>
#include <cmath>
#include <complex>
#include <algorithm>
#include <numeric>
#include <utility>
#include <tuple>
#include <bitset>
#include <cstdint>
#include <cassert>
#include <random>
#include <iterator>

using namespace std;
using i64 = int64_t;
using i32 = int32_t;

struct WeightedUnionFind {
    vector<int> p, s;
    vector<i64> w;
    WeightedUnionFind(size_t n) : p(n, -1), s(n, 1), w(n, 0) {}
    int root(int u) { 
        while (p[u] != -1) u = p[u];
        return u;
    }
    bool same(int u, int v) {
        return root(u) == root(v);
    }
    bool unite(int u, int v, i64 d) {
        int ru = root(u), rv = root(v);
        if (ru != rv) {
            if (s[ru] < s[rv]) {
                swap(u, v);
                swap(ru, rv);
                d = -d;
            }
            p[rv] = ru;
            s[ru] += s[rv];
            w[rv] = diff_to_root(u) - diff_to_root(v) - d;
            return true;
        } else {
            return diff(u, v).second == d;
        }
    }
    int size(int i) {
        return s[root(i)];
    }
    i64 diff_to_root(int u) {
        i64 d = 0;
        for (; p[u] != -1; u = p[u]) d += w[u];
        return d;
    }
    pair<bool, i64> diff(int u, int v) {
        if (!same(u, v)) return { false, 0 };
        return { true, diff_to_root(u) - diff_to_root(v) };
    }
};

int main() {
    int n, q;
    cin >> n >> q;
    WeightedUnionFind uf(n);
    while (q--) {
        int cmd;
        cin >> cmd;
        if (cmd == 0) {
            int x, y, z;
            cin >> x >> y >> z;
            assert(uf.unite(x, y, z));
        } else {
            int x, y;
            cin >> x >> y;
            auto p = uf.diff(x, y);
            if (p.first) {
                cout << p.second << '\n';
            } else {
                cout << "?\n";
            }
        }
    }
    return 0;
}