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<cstdio>
#include<iostream>
#include<algorithm>
#include<utility>
#include<vector>
#include<queue>
#include<functional>
#include<map>
#include<set>
#include<cstring>
#include<string>
#include<stack>
#include<math.h>
#include<stdlib.h>
using namespace std;
#define int long long
//#define double long double
typedef pair<int, int> pii;
typedef pair<pii, int> ppi;
typedef pair<int, pii > pip;
typedef pair<pii, pii > piipii;
typedef pair<double, double> pdd;
typedef pair<int, char> pic;
typedef priority_queue<pii, vector<pii>, greater<pii> > RPQ;
#define all(vec) vec.begin(), vec.end()
#define mk make_pair
#define INF (1 << 30)
#define INFL (1ll << 60)
#define mod 1000000007
#define se second
#define fi first

int N, Q;

int par[100100];
int rnk[100100];
int dif[100100];

void init(){
    for(int i = 0; i < N; i++){
        par[i] = i;
        rnk[i] = 0;
        dif[i] = 0;
    }
}

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

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

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

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

bool unite(int x, int y, int w){
    w += weight(x);
    w -= weight(y);

    x = root(x);
    y = root(y);

    if(rnk[x] < rnk[y]){
        swap(x, y);
        w = -w;
    }
    if(rnk[x] == rnk[y]){
        rnk[x]++;
    }
    par[y] = x;

    dif[y] = w;

    return true;
}

signed main(){
    cin >> N >> Q;
    init();
    for(int i = 0; i < Q; i++){
        int c, x, y, z;
        cin >> c >> x >> y;
        if(c){
            if(!same(x, y)){
                cout << "?" << endl;
            }
            else cout << diff(x, y) << endl;
        }
        else {
            cin >> z;
            unite(x, y, z);
        }
    }
    
    return 0;
}

/*

*/