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<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using P = pair<ll, ll>;
ll GCD(ll a, ll b) { return b?GCD(b, a%b):a; }
ll LCM(ll a, ll b) { return a/GCD(a, b)*b; }

template<class Abel> struct UnionFind {
    vector<int> par;
    vector<int> rank;
    vector<Abel> diff_weight;

    UnionFind(int n = 1, Abel SUM_UNITY = 0) {
        init(n, SUM_UNITY);
    }

    void init(int n = 1, Abel SUM_UNITY = 0) {
        par.resize(n); rank.resize(n); diff_weight.resize(n);
        for(int i = 0; i < n; ++i) {
            par[i] = i; rank[i] = 0; diff_weight[i] = SUM_UNITY;
        }
    }

    int find(int x) {
        if(par[x] == x) return x;
        else {
            int r = find(par[x]);
            diff_weight[x] += diff_weight[par[x]];  // 累積和を取る
            return par[x] = r;
        }
    }

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

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

    bool unite(int x, int y, Abel w) {
        w += weight(x); w -= weight(y); // xとyそれぞれについて、rootとの重み差分を補正
        x = find(x); y = find(y);
        if(x == y) return false;
        if(rank[x] < rank[y]) swap(x, y), w = -w;   // rank[x] >= rank[y]になるようにswap
        if(rank[x] == rank[y]) ++rank[x];
        par[y] = x;
        diff_weight[y] = w; // xがyの親になるので、xとyの差分をdiff_weight[y]に記録
        return true;
    }

    // 重みを取得する
    Abel diff(int x, int y) {
        return weight(y) - weight(x);
    }
};

int main() {
    int n, q; cin >> n >> q;
    UnionFind<int> uf(n);
    for(int i = 0; i < q; ++i) {
        int c, x, y, z;
        cin >> c >> x >> y;
        if(c) {
            if(uf.same(x, y)) cout << uf.diff(x, y) << endl;
            else cout << "?" << endl;
        }else {
            cin >> z;
            uf.unite(x, y, z);
        }
    }
}