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>
#define REP(i, a) for(int i=0; i<int(a); i++)
#define ALL(x) begin(x), end(x)
#define VI vector<int>
using namespace std;
typedef long long LL;

const int MAX_N=100005;

struct WeightedUnionFind {
    int n;
    int INF = 1e9;
    vector<int> par, sz, weight;

    WeightedUnionFind() {}
    WeightedUnionFind(int n_) : n(n_), par(n_, 0), sz(n_, 1), weight(n_, 0) { iota(begin(par), end(par), 0); }

    int find(int x) { 
        if(x==par[x]) return x;
        int y = find(par[x]);
        weight[x]+=weight[par[x]];
        return par[x]=y;
    }

    void unite(int x, int y, int w) {
        int px = find(x);
        int py = find(y);
        if(px == py) return;
        if(sz[px] < sz[py]) {
            swap(px, py);
            swap(x, y);
            w = -w;
        }
        sz[px] += sz[py];
        par[py] = px;
        weight[py] = weight[x] - w - weight[y];            
    }

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

    int diff(int x, int y) { // x -> y
        if(same(x, y)) return weight[x]-weight[y];
        return INF;
    }
};

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

    while(q--) {
        int op;
        cin >> op;
        if(op == 0) {
            int x, y, w;
            cin >> x >> y >> w;
            wuf.unite(x, y, w);
        } else {
            int x, y;
            cin >> x >> y;
            int ans = wuf.diff(x,y);
            if(ans < wuf.INF) cout << ans << endl;
            else cout << '?' << endl;
        }
    }

    return 0; 
}