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 <algorithm>
#include <vector>
#include <iomanip>
#include <map>
#include <queue>

static const int MOD = 1000000007;
using ll = long long;
using u32 = unsigned;
using namespace std;

template<class T>
constexpr T INF = ::numeric_limits<T>::max() / 2 - 170;

template <class T>
class WeightedUnionFind {
    vector<int> uni;
    vector<T> weights;
    int n;
public:
    explicit WeightedUnionFind(int n, T SUM_UNITY = 0) :
    uni(static_cast<u32>(n), -1) , n(n), weights(n,  SUM_UNITY){};

    int root(int a) {
        if (uni[a] < 0) return a;
        else {
            int r = root(uni[a]);
            weights[a] += weights[uni[a]];
            return (uni[a] = r);
        }
    }

    bool unite(int a, int b, T w) {
        w += weight(a); w -= weight(b);
        a = root(a);
        b = root(b);
        if(a == b) return false;
        if(uni[a] > uni[b]) swap(a, b), w = -w;
        uni[a] += uni[b];
        uni[b] = a;
        weights[b] = w;
        return true;
    }

    int size(int a){
        return -uni[root(a)];
    }

    T weight(T a){
        root(a);
        return weights[a];
    }
    int diff(int x, int y){
        return weight(y) - weight(x);
    }
};



int main() {
    int n, q;
    cin >> n >> q;
    WeightedUnionFind<ll> u(n);
    for (int i = 0; i < q; ++i) {
        int a, x, y;
        ll w;
        scanf("%d", &a);
        if(a) {
            scanf("%d%d", &x, &y);
            if(u.root(x) != u.root(y)){
                printf("?\n");
            }else {
                printf("%d\n", u.diff(x, y));
            }
        }
        else {
            scanf("%d%d%lld", &x, &y, &w);
            u.unite(x, y, w);
        }
    }
    return 0;
}