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;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vll = vector<ll>;
using vvll = vector<vll>;
const double eps = 1e-8;
const int MOD = 1000000007;
// int main() {
//     cin.tie(0);
//     ios::sync_with_stdio(false);
//     cout << fixed << setprecision(10);
//
// }
template<typename A>
struct WeightedUnionFind
{
    vector<int> par, sz;
    vector<A> data; // data[x]: diff from root to x
    WeightedUnionFind(int n, A e=0) :
        par(n), sz(n, 1), data(n, e) {
        for (int i = 0; i < n; ++i) par[i] = i;
    }
    int root(int x) {
        if (par[x] == x) return x;
        int r = root(par[x]);
        data[x] += data[par[x]];
        return par[x] = r;
    }
    A weight(int x) {
        root(x);
        return data[x];
    }
    A diff(int x, int y) {
        // diff from x to y
        return data[y] - data[x];
    }
    void merge(int x, int y, A w) {
        // merge so that "diff from x to y" will be w.
        w += weight(x); w -= weight(y);
        x = root(x); y = root(y);
        if (x == y) return;
        if (sz[x] < sz[y]) swap(x, y), w = -w;
        par[y] = x;
        sz[x] += sz[y];
        sz[y] = 0;
        data[y] = w;
    }
    bool issame(int x, int y) {
        return root(x) == root(y);
    }
};
int main() {
    int N, M;
    cin >> N >> M;
    WeightedUnionFind<int> uf(N);
    while (M--) {
        int A, B, C, D;
        cin >> A >> B >> C;
        if (A == 0) {
            cin >> D;
            uf.merge(B, C, D);
        } else {
            if (uf.root(B) == uf.root(C)) {
                cout << uf.diff(B, C) << endl;
            } else {
                cout << "?" << endl;
            }
        }
    }
}