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>
using namespace std;

using T = int;
const T id = INT_MAX;
T op(T l, T r) {
	return min(l, r);
}

struct node;
node *update(node *t);

struct node {
	T val, all;
	node *ch[2];
	int dep, size;
	node() {}
	void init(T v) {
		val = all = v;
		dep = size = 1;
		ch[0] = ch[1] = nullptr;
	}
	void init(node* l, node* r) {
		val = id;
		ch[0] = l, ch[1] = r;
		update(this);
	}
};

const int pmax = 1e6;
node pool[pmax];
queue<int> deleted;
int it = 0;

int depth(node *t) { return t ? t->dep : 0; }
int count(node *t) { return t ? t->size : 0; }
int que(node *t) { return t ? t->all : id; }

node *new_leaf(T v) {
	if (!deleted.empty()) {
		auto pos = deleted.front(); deleted.pop();
		pool[pos].init(v);
		return pool + pos;
	}
	assert(it < pmax);
	pool[it].init(v);
	return pool + it++;
}

node *new_node(node *l, node *r) {
	if (!deleted.empty()) {
		auto pos = deleted.front(); deleted.pop();
		pool[pos].init(l, r);
		return pool + pos;
	}
	assert(it < pmax);
	pool[it].init(l, r);
	return pool + it++;
}

void delete_node(node* t) {
	deleted.push(t - pool);
}

node *update(node *t) {
	t->dep = max(depth(t->ch[0]), depth(t->ch[1])) + 1;
	t->all = op(que(t->ch[0]), op(t->val, que(t->ch[1])));
	t->size = count(t->ch[0]) + count(t->ch[1]) + (!t->ch[0] || !t->ch[1]);
	return t;
}

node *rotate(node *t, int b) {
	node *s = t->ch[1 - b];
	t->ch[1 - b] = s->ch[b];
	s->ch[b] = t;
	t = update(t);
	s = update(s);
	return s;
}

node *fix(node *t) {
	if (!t) return t;
	int dd = depth(t->ch[0]) - depth(t->ch[1]);
	if (abs(dd) < 2) return t;
	int b = dd < 0;
	if (depth(t->ch[b]->ch[!b]) > depth(t->ch[b]->ch[b])) {
		t->ch[b] = rotate(t->ch[b], b);
	}
	return rotate(t, !b);
}

node *submerge(node *l, node *r) {
	if (l->dep == r->dep) return new_node(l, r);
	if (l->dep < r->dep) {
		r->ch[0] = submerge(l, r->ch[0]);
		return fix(update(r));
	}
	l->ch[1] = submerge(l->ch[1], r);
	return fix(update(l));
}

node *merge(node *l, node *r) {
	if (!l) return r;
	if (!r) return l;
	return submerge(l, r);
}

pair<node*, node*> split(node *t, int k) {
	if (!t) return make_pair(nullptr, nullptr);
	if (k == 0) return make_pair(nullptr, t);
	if (k >= count(t)) return make_pair(t, nullptr);
	int c = count(t->ch[0]);
	node *l = t->ch[0], *r = t->ch[1];
	delete_node(t);
	if (k < c) {
		pair<node*, node*> p = split(l, k);
		return make_pair(p.first, merge(p.second, r));
	}
	if (k > c) {
		pair<node*, node*> p = split(r, k - c);
		return make_pair(merge(l, p.first), p.second);
	}
	return make_pair(l, r);
}

node *insert(node *t, int k, T v) {
	pair<node*, node*> s = split(t, k);
	return merge(merge(s.first, new_leaf(v)), s.second);
}

node *erase(node *t, int k) {
	pair<node*, node*> s1 = split(t, k), s2 = split(s1.second, 1);
	return merge(s1.first, s2.second);
}

node *find(node *t, int k) {
	if (!t) return t;
	int c = count(t->ch[0]), b = (!t->ch[0] || !t->ch[1]);
	return c == 0 && b ? t : k < c ? find(t->ch[0], k) : find(t->ch[1], k - c - b);
}

T find(node *t, int l, int r) {
	if (!t) return id;
	if (r < 0 || l >= count(t)) return id;
	if (l <= 0 && r >= t->size) return t->all;
	int c = count(t->ch[0]), d = c + (!t->ch[0] || !t->ch[1]);
	return op(!t->ch[0] ? id : find(t->ch[0], l, r), op(l <= c && c < r ? t->val : id, !t->ch[1] ? id : find(t->ch[1], l - d, r - d)));
}

void update(node *t, int k, T val) {
	if (!t) return;
	int c = count(t->ch[0]), b = (!t->ch[0] || !t->ch[1]);
	if (c == 0 && b) {
		t->val = val;
	}
	else if (k < c) {
		update(t->ch[0], k, val);
	}
	else {
		update(t->ch[1], k - c - b, val);
	}
	update(t);
}

node* build(const vector<T>& a, int lb, int ub) {
	if (ub - lb == 1) return new_leaf(a[lb]);
	int m = (lb + ub) >> 1;
	return merge(build(a, lb, m), build(a, m, ub));
}

int main()
{
	ios::sync_with_stdio(false), cin.tie(0);
	int n, q;
	cin >> n >> q;
	vector<T> a(n);
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	node* root = build(a, 0, n);
	while (q--) {
		int x, y, z;
		cin >> x >> y >> z;
		if (x == 0) {
			int val = find(root, z)->val;
			root = insert(erase(root, z), y, val);
		}
		else if (x == 1) {
			printf("%d\n", find(root, y, z + 1));
		}
		else {
			update(root, y, z);
		}
	}
	return 0;
}