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;
typedef long long ll;

struct UnionFind{
    vector<int> parent;
    vector<ll> dist;
    UnionFind(int x = 1){
        parent.clear(); parent.resize(x,-1);
        dist.clear(); dist.resize(x,0);
    }
    int find(int x){
        if(parent[x]<0)return x;
        int r = find(parent[x]);
        dist[x]+=dist[ parent[x] ];
        return parent[x]=r;    
    }
    ll depth(int x) { find(x); return dist[x]; }

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

    int size(int x) { return -parent[find(x)]; }

    void unite(int x,int y,ll k=0){
        k+=depth(y);
        k-=depth(x);
        k*=-1;
        x=find(x);
        y=find(y);
        if(x==y)return;
        if(size(x)<size(y)) { swap(x,y); k *= -1;}
        parent[x]+=parent[y];
        parent[y]=x;
        dist[y]=k;
    }
};


int main(){
    int n,q; cin >> n >> q;
    UnionFind T(n);
    for(int i=0;i<q;i++){
        int type,x,y;
        scanf("%d %d %d",&type,&x,&y);
        if(type==0){
            int a;
            scanf("%d",&a);
            T.unite(x,y,a);
        }
        else{
            if(!T.same(x,y)) printf("?\n");
            else printf("%lld\n",T.depth(x)-T.depth(y));
        }
    }
    return 0;
}