Problem: Given n numbers a0, a1, ..., an-1 and q.
I want you to perform appropriate processing for q queries.
The query has the following three types of operations.


* Shift the value
Given a pair of l and r. (l <r) Circular shift the value from al to ar.

0 1 2 3 4 5 6 7 8 9

Is given the query l = 2, r = 5.

The shifted number sequence is

0 1 5 2 3 4 6 7 8 9

Will be.


* Find the minimum value
Given a pair of l and r. (l ≤ r)
Find the smallest value from al to ar.


* Update value
Given a pair of pos and val. Update the value of apos to val.



Input

The input is given in the following format.


n q
a0
a1
..
..
..
an-1
x1 y1 z1
x2 y2 z2
..
..
..
xq yq zq


If xi = 0, it represents a shift query. At this time, let l = yi and r = zi.
If xi = 1, it represents a query for the minimum value. At this time, let l = yi and r = zi.
If xi = 2, it represents a query that updates the value. At this time, pos = yi, val = zi.


Input meets the following constraints
1 ≤ n, q ≤ 200,000
0 ≤ ai ≤ 10,000,000 For queries that update values, 0 ≤ val ≤ 10,000,000

Output

When xi = 1 is given as a query, output the value of the answer on one line.

Examples

Input

10 3
0
1
2
3
4
5
6
7
8
9
1 5 7
0 2 5
1 5 7


Output

5
4


Input

10 10
289383
930886
692777
636915
747793
238335
885386
760492
516649
641421
2 7 368690
1 3 6
0 2 6
1 1 8
0 2 9
2 2 665123
1 5 9
0 2 8
2 7 961393
1 1 2


Output

238335
238335
238335
368690

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

#define _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)

#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)

#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))

using namespace std;

template<class T>bool chmax(T &a, const T &b) { return (a<b)?(a=b,1):0;}
template<class T>bool chmin(T &a, const T &b) { return (b<a)?(a=b,1):0;}

using ll=long long;
using R=long double;
const R EPS=1e-9; // [-1000,1000]->EPS=1e-8 [-10000,10000]->EPS=1e-7
inline int sgn(const R& r){return(r > EPS)-(r < -EPS);}
inline R sq(R x){return sqrt(max<R>(x,0.0));}

const int dx[8]={1,0,-1,0,1,-1,-1,1};
const int dy[8]={0,1,0,-1,1,1,-1,-1};


// Treap based on merge and split 
// each operation 
// set parameter
const int inf=1<<29;
const int nmax=1000010;

mt19937 mt;   
uniform_real_distribution<double> rnd(0.0,1.0);

struct Node{
	int val,cnt,min,add,rev;
	Node *lch=nullptr,*rch=nullptr;
	double pri;
	Node(){}
	Node(int v): val(v),cnt(1),min(v),add(0),rev(0),pri(rnd(mt)){}
};

// memory pool
int total=0;
Node pool[nmax];

Node* create(int v){
	pool[total]=Node(v);
	return &(pool[total++]);	
}

// helper function
int val(Node* x){assert(x!=nullptr); return x->val+x->add;}
int cnt(Node* x){return (x==nullptr)?0:x->cnt;}
int min(Node* x){return (x==nullptr)?inf:x->min+x->add;}

Node* update(Node* x){
	if(x==nullptr) return x;
	
	x->cnt=1+cnt(x->lch)+cnt(x->rch);
	x->min=min({val(x),min(x->lch),min(x->rch)});

	if(x->add) {
		x->val+=x->add;
		if(x->lch!=nullptr) x->lch->add+=x->add;
		if(x->rch!=nullptr) x->rch->add+=x->add;
		x->add=0;
	}

	if(x->rev) {
		swap(x->lch,x->rch);
		if(x->lch!=nullptr) x->lch->rev^=true;
		if(x->rch!=nullptr) x->rch->rev^=true;
		x->rev=false;
	}
	
	return x;
}

Node* merge(Node* l,Node* r){
	l=update(l),r=update(r);
	if(l==nullptr) return r;
	if(r==nullptr) return l;
	
	if(l->pri > r->pri){
		l->rch = merge(l->rch,r);
		return update(l);
	}else{
		r->lch = merge(l,r->lch);
		return update(r);
	}
}

tuple<Node*,Node*> split(Node* x,int k){ //[0,k) [k,n)
	x=update(x);
	if(x==nullptr) return make_tuple(nullptr,nullptr);

	Node *l,*r;
	if(k<=cnt(x->lch)){
		tie(l,r)=split(x->lch,k);
		x->lch=r;
		return make_tuple(update(l),update(x));
	}else{
		tie(l,r)=split(x->rch,k-cnt(x->lch)-1);
		x->rch=l;
		return make_tuple(update(x),update(r));
	}
}

Node* range_merge(Node* left,Node* tar,Node* right){
	return merge(left,merge(tar,right));
}

tuple<Node*,Node*,Node*> range_split(Node* t,int l,int r){
	Node *left,*tar,*right; 
	tie(tar,right)=split(t,r);
	tie(left,tar)=split(tar,l);
	return make_tuple(left,tar,right);
}

void insert(Node* &t,int k,int v){
	Node *left,*right,*tar=create(v);
	tie(left,right)=split(t,k);
	t=range_merge(left,tar,right);
}

void erase(Node* &t,int k){
	Node *left,*tar,*right;
	tie(left,tar,right)=range_split(t,k,k+1);
	t=merge(left,right);
}

void shift(Node* &t,int l,int r){
	Node *left,*tar,*right; 
	tie(left,tar,right)=range_split(t,l,r);
	Node *tar_l,*tar_r;
	tie(tar_l,tar_r)=split(tar,cnt(tar)-1);
	tar=merge(tar_r,tar_l);
	t=range_merge(left,tar,right);
}

int min(Node* &t,int l,int r){
	Node *left,*tar,*right; 
	tie(left,tar,right)=range_split(t,l,r);
	int ret=tar->min;
	t=range_merge(left,tar,right);
	return ret;
}

void change(Node* &t,int p,int v){
	erase(t,p);
	insert(t,p,v);
}

int main(void){
	int n,q;
	cin >> n >> q;
	
	Node* t=nullptr;

	rep(i,n){
		int in;
		cin >> in;
		t=merge(t,create(in));
	}	

	rep(loop,q){
		int type,a,b;
		cin >> type >> a >> b;
		if(type==0)
			shift(t,a,b+1);
		else if(type==1)
			cout << min(t,a,b+1) << endl;
		else
			change(t,a,b);
	}
	return 0;
}