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;
const int mod = 1e9 + 7;
const int inf = (1 << 30) - 1;
const ll infll = (1LL << 61) - 1;

#include <vector>

template <typename T>
struct WeightedUnionFind
{
    vector<int> data;
    vector<T> weight_diff;


    WeightedUnionFind(int sz) : data(sz, -1), weight_diff(sz) {}

    int find(int k)
    {
        if (data[k] < 0)
            return k;
        auto par = find(data[k]);
        weight_diff[k] += weight_diff[data[k]];
        return data[k] = par;
    }

    T weight(int t)
    {
        find(t);
        return weight_diff[t];
    }

    bool unite(int x, int y, T w)
    {
        w += weight(x);
        w -= weight(y);
        x = find(x), y = find(y);
        if (x == y)
            return false;
        if (data[x] > data[y])
        {
            swap(x, y);
            w *= -1;
        }
        data[x] += data[y];
        data[y] = x;
        weight_diff[y] = w;
        return true;
    }

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

    bool same(int x, int y)
    {
        return (find(x) == find(y));
    }
};

int main()
{
    int N, q;
    cin >> N >> q;
    WeightedUnionFind<int> uf(N);
    for (int i = 0; i < q; i++)
    {
        int a;
        cin >> a;
        if (a == 0)
        {
            int x, y, z;
            cin >> x >> y >> z;
            uf.unite(x, y, z);
        }
        else
        {
            int x, y;
            cin >> x >> y;
            if (uf.same(x, y) == true)
            {
                cout << uf.diff(x, y) << endl;
            }
            else
            {
                cout << "?" << endl;
            }
        }
    }
}