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:
//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;


template<class Abel>
struct wUnionFind {
    vector<int> par;
    vector<Abel> diff_weight;
    wUnionFind(int n):par(n, -1), diff_weight(n) {}
    int root(int x) {
        if(par[x] < 0) return x;
        int r = root(par[x]);
        diff_weight[x] += diff_weight[par[x]];
        return par[x] = r;
    }
    bool unite(int x, int y, Abel w) { //weight(y) - weight(x) = w となるようにする
        w += weight(x)-weight(y);
        x = root(x); y = root(y);
        if(x == y) {
            assert(diff(x, y) == w);
            return false;
        }
        if(par[x] > par[y]) swap(x, y), w = -w;
        par[x] += par[y];
        par[y] = x;
        diff_weight[y] = w;
        return true;
    }
    bool same(int x, int y) {return root(x) == root(y);}
    bool size(int x) {return -par[root(x)];}
    Abel weight(int x) {
        root(x);
        return diff_weight[x];
    }
    Abel diff(int x, int y) {
        assert(same(x, y));
        return weight(y)-weight(x);
    }
};

int main() {
    int n, q;
    cin >> n >> q;
    wUnionFind<int> wuft(n);
    while(q--) {
        int t;
        cin >> t;
        if(t) {
            int x, y;
            cin >> x >> y;
            if(wuft.same(x, y)) {
                cout << wuft.diff(x, y) << '\n';
            } else {
                cout << '?' << '\n';
            }
        } else {
            int x, y, z;
            cin >> x >> y >> z;
            wuft.unite(x, y, z);
        }
    }
}