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 <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <tuple>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <cmath>
#include <iomanip>
#define rep(i, n) for(int i = 0; i < (int)(n); ++i)
using namespace std;
using lint = int64_t;

struct WeightedUnionFind {
    vector<int> par, wei;
    WeightedUnionFind (int N) : par(N, -1), wei(N, 0) {}
    int root(int x) {
        if (par[x] < 0) {
            return x;
        } else {
            int rx = root(par[x]);
            wei[x] += wei[par[x]];
            return par[x] = rx;
        }
    }
    bool same(int x, int y) {
        return root(x) == root(y);
    }
    int weight(int x) {
        root(x);
        return wei[x];
    }
    int diff(int x, int y) {
        return weight(y) - weight(x);
    }
    bool unite(int x, int y, int w) {
        int rx = root(x);
        int ry = root(y);
        if (rx == ry) return diff(x, y) == w;
        w += wei[x];
        w -= wei[y];
        if (par[rx] > par[ry]) {
            swap(rx, ry);
            w = -w;
        }
        par[rx] += par[ry];
        par[ry] = rx;
        wei[ry] = w;
        return true;
    }
};

int main() {
    int n;
    cin >> n;
    WeightedUnionFind WUF(n);
    int q;
    cin >> q;
    rep(i, q) {
        int num;
        cin >> num;
        if (num == 0) {
            int x, y, z;
            cin >> x >> y >> z;
            WUF.unite(x, y, z);
        } else {
            int x, y;
            cin >> x >> y;
            if (WUF.same(x, y)) cout << WUF.diff(x, y) << "\n";
            else cout << "?\n";
        }
    }
    return 0;
}