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 Abel>
struct WeightedUnionFind{
    int num;
    vector<int> par,rank;
    vector<Abel> diff_weight;
    WeightedUnionFind(int n,Abel id=0):
        num(n),par(n),rank(n,1),diff_weight(n,Abel(0)){
        iota(par.begin(),par.end(),0);
    }
    int root(int x){
        if (x==par[x]) return x;
        int t=root(par[x]);
        diff_weight[x]+=diff_weight[par[x]];
        return par[x]=t;
    }
    bool merge(int x,int y,Abel w){
        w+=weight(x),w-=weight(y);
        x=root(x),y=root(y);
        if (x==y) return false;
        if (rank[x]<rank[y]) swap(x,y),w=-w;
        par[y]=x;
        rank[x]+=rank[y];
        diff_weight[y]=w;
        --num;
        return true;
    }
    Abel weight(int x){
        root(x);
        return diff_weight[x];
    }
    Abel diff(int x,int y){return weight(y)-weight(x);}
    bool same(int x,int y){return root(x)==root(y);}
    int size(int x){return rank[root(x)];}
    int count(){return num;}
};

// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/1/DSL_1_B

void DSL_1_B(){
    int n,q; cin >> n >> q;
    WeightedUnionFind<int> uf(n);
    for (;q--;){
        int c,x,y,z; cin >> c >> x >> y;
        if (!c){
            cin >> z;
            uf.merge(x,y,z);
        } else {
            if (uf.same(x,y)) cout << uf.diff(x,y) << '\n';
            else cout << '?' << '\n';
        }
    }
}

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    DSL_1_B();
}