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>
#include<algorithm>
#include<cctype>
#include<utility>
#include<string>
#include<cmath>
#include <numeric>
#include<map>
 
 
#define REP(i, n) for(int i = 0;i < n;i++)
#define REPR(i, n) for(int i = n;i >= 0;i--)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define FORR(i, m, n) for(int i = m;i >= n;i--)
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define llong long long
#define pb(a) push_back(a)
#define INF 1e13
using namespace std;
typedef pair<int, int> P;
typedef pair<llong, llong> LP;
typedef pair<int, P> PP;
typedef pair<llong, LP> LPP;
 
typedef long long int ll;
#define MOD 1000000007


struct Potential_UnionFind{
    vector<int> par;
    vector<int> rank;
    vector<int> diff_weight;

    void init(int n) {
        par.resize(n);
        rank.resize(n);
        diff_weight.resize(n);
        REP(i,n){
            par[i] = i;
            rank[i] = 0;
            diff_weight[i] = 0;
        }
    }

    int root(int x) {
        if (par[x] == x) {
            return x;
        }
        else {
            int r = root(par[x]);
            diff_weight[x] += diff_weight[par[x]];
            return par[x] = r;
        }
    }

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

    bool issame(int x,int y) {
        return root(x) == root(y);
    }

    void merge(int x, int y,int w) {
        w += weight(x); w -= weight(y);
        x = root(x); y = root(y);
        if (x == y) return;
        if (rank[x] < rank[y]) swap(x, y), w = -w;
        if (rank[x] == rank[y]) ++rank[x];
        par[y] = x;
        diff_weight[y] = w;
    }

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

Potential_UnionFind PUF;

int main(){

    int n,q;
    cin >> n >> q;
    PUF.init(n);
    
    REP(i,q){

        int num,x,y,z;
        cin >> num;
        if(!num){
            //mergeする
            cin >> x >> y >> z;
            PUF.merge(x,y,z);     

        }else{
            //diffを求める

            cin >> x >> y;
            if(!PUF.issame(x,y)){
                cout << "?" << endl;
            }else{
                cout << PUF.diff(x,y) << endl;
            }
        }
    }
    return 0;
}