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 <vector>
using namespace std;

class WeightedUnionFind {
public:
    vector<int> parents, rank, diff_weight;

    WeightedUnionFind(int n) : parents(n), rank(n), diff_weight(n) {
        for (int i = 0; i < n; i++) {
            parents[i] = i;
            rank[i] = 0;
            diff_weight[i] = 0;
        }        
    }

    int root(int x) {
        if (parents[x] == x) { // root
            return x;
        } else {
            int r = root(parents[x]);
            diff_weight[x] += diff_weight[parents[x]];
            return parents[x] = r;
        }
    }

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

    bool unite(int x, int y, int w) {
        w += weight(x); w -= weight(y);
        x = root(x); y = root(y);
        if (x == y) return false;

        if (rank[x] < rank[y]) {
            swap(x, y);
            w = -w;
        }

        if (rank[x] == rank[y]) ++rank[x];
        parents[y] = x;

        diff_weight[y] = w;

        return true;
    }

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

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

int main(void) {

    int n, q; cin >> n >> q;
    WeightedUnionFind wuf(n);

    for (int i = 0; i < q; i++) {
        int type; cin >> type;
        if (type == 0) {
            int x, y, z; cin >> x >> y >> z;            
            wuf.unite(x, y, z);
        } else if (type == 1) {
            int x, y; cin >> x >> y;
            if (!wuf.isSame(x, y)) cout << "?" << endl;
            else cout << wuf.diff(x, y) << endl;
        }
    }

    return 0;
}