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;

template<typename T>
struct WeightedUnionFind {
    const int V;
	// par[x] := xのroot
	vector<int> par;
	// sz[x] := xを含む集合のサイズ
	vector<int> sz;
    // w[x] := xのrootに対する重み
    vector<T> w;
    WeightedUnionFind(const int V) :
		V(V),
		par(vector<int>(V)),
		sz(vector<int>(V, 1)),
		w(vector<T>(V))
		{
			for(int i = 0; i < V; ++i) par[i] = i;
		}
    // w[y] - w[x] = z
    bool unite(int x, int y, T z) {
        z = z + weight(x) - weight(y);
        x = root(x), y = root(y);
        if(same(x, y)) return false;
        if(y < x) {
            swap(x, y);
            z = -z;
        }
        par[y] = x;
        sz[x] += sz[y];
        w[y] = z;
        return true;
    }
    int root(int x) {
    	if(par[x] == x) return x;
        root(par[x]); // rootから累積和
        w[x] += w[par[x]]; // 親の重みを加算する
    	return (par[x] = root(par[x])); // xの親のroot
    }
    bool same(int x, int y) {
    	return (root(x) == root(y));
    }
    int size(int x) {
        return sz[root(x)];
    }
    T weight(int x) {
        root(x); // 経路圧縮用
        return w[x];
    }
    T diff(int x, int y) {
        assert(same(x, y));
        return weight(y) - weight(x);
    }
};

int main() {
    int n, q; cin >> n >> q;
    WeightedUnionFind<int64_t> uf(n);
    while(q--) {
        int info, x, y, z; cin >> info >> x >> y;
        if(info == 0) {
            cin >> z;
            uf.unite(x, y, z);
        } else {
            if(uf.same(x, y)) {
                cout << uf.diff(x, y) << '\n';
            } else {
                cout << '?' << '\n';
            }
        }
    }
    return 0;
}