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 <vector>

using namespace std;

// (weighted) UnionFind
class UnionFind {
    public:
        UnionFind(int n) : mPar(n), mRnk(n,0), mWeight(n,0) {
            for(int i = 0; i < n; ++i) mPar[i] = i;
        }

        int find(int x){
            if(mPar[x]==x) return x;
            int r = find(mPar[x]); // 経路圧縮
            mWeight[x] += mWeight[mPar[x]]; // 一つ上の親からの累積和
            return mPar[x] = r;
        }

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

        int weight(int x){
            find(x); // 経路圧縮
            return mWeight[x];
        }

        int diff(int x, int y){
            return weight(y) - weight(x);
        }

        void unite(int x,int y, int w = 0){
            w += weight(x); w -= weight(y);
            x = find(x);
            y = find(y);
            if(x==y) return;
            if(mRnk[x] < mRnk[y]) swap(x,y), w = -w;
            mPar[y] = x;
            mWeight[y] = w;
            if(mRnk[x] == mRnk[y]) ++mRnk[x];
        }

    private:
        vector<int> mPar, mRnk, mWeight;
};

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