Go: package main

// packed from [splaytree.go main.rmq.go splaytree_debug.go] with goone.

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

type SplayTreeNode struct {
	parent, left, right *SplayTreeNode

	size    int
	value   int
	minimum int
}

func newSplayTreeNode(v int) *SplayTreeNode {
	return &SplayTreeNode{value: v}
}

func (node *SplayTreeNode) rotate() {
	var pp, p, c *SplayTreeNode
	p = node.parent
	pp = p.parent
	if pp != nil && pp.left == p {
		pp.left = node
	}
	if pp != nil && pp.right == p {
		pp.right = node
	}
	node.parent = pp
	if p.left == node {
		c = node.right
		node.right = p
		p.left = c
	} else {
		c = node.left
		node.left = p
		p.right = c
	}
	p.parent = node
	if c != nil {
		c.parent = p
	}
	p.update()
	node.update()
}

func (node *SplayTreeNode) state() int {
	if node.parent == nil {
		return 0
	}
	if node.parent.left == node {
		return -1
	} else if node.parent.right == node {
		return 1
	}
	return 0
}

func (node *SplayTreeNode) splay() {
	for node.state() != 0 {
		if node.parent.state() == 0 {
			node.rotate()
			return
		}
		if node.state() == node.parent.state() {
			node.parent.rotate()
			node.rotate()
		} else {
			node.rotate()
			node.rotate()
		}
	}
}

func (node *SplayTreeNode) update() {
	node.size = 1
	node.minimum = node.value
	if node.left != nil {
		node.size += node.left.size
		node.minimum = min(node.minimum, node.left.minimum)
	}
	if node.right != nil {
		node.size += node.right.size
		node.minimum = min(node.minimum, node.right.minimum)
	}
}
func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func (node *SplayTreeNode) Get(idx int) *SplayTreeNode {
	cur := node
	for true {
		lSize := 0
		if cur.left != nil {
			lSize = cur.left.size
		}
		if idx < lSize {
			cur = cur.left
		}
		if lSize == idx {
			cur.splay()
			return cur
		}
		if idx > lSize {
			cur = cur.right
			idx = idx - lSize - 1
		}
	}
	return nil
}

func mergeSplayNode(l, r *SplayTreeNode) (root *SplayTreeNode) {
	if l == nil {
		return r
	}
	if r == nil {
		return l
	}
	root = l.Get(l.size - 1)
	root.right = r
	r.parent = root
	root.update()
	return root
}

func (node *SplayTreeNode) Split(leftCount int) (left *SplayTreeNode, right *SplayTreeNode) {
	root := node.Get(leftCount)
	lRoot, rRoot := root.left, root

	rRoot.left = nil
	if lRoot != nil {
		lRoot.parent = nil
	}
	rRoot.update()
	return lRoot, rRoot
}

func splayTreeInsert(t *SplayTreeNode, idx int, node *SplayTreeNode) (root *SplayTreeNode) {
	l, r := t.Split(idx)
	return mergeSplayNode(
		mergeSplayNode(l, node),
		r,
	)
}

func removeSplayTree(t *SplayTreeNode, idx int) (root *SplayTreeNode, removed *SplayTreeNode) {
	target := t.Get(idx)
	l, r := target.left, target.right
	if l != nil {
		l.parent = nil
	}
	if r != nil {
		r.parent = nil
	}
	target.left = nil
	target.right = nil
	target.update()
	return mergeSplayNode(l, r), target
}

const (
	initialBufSize = 100000
	maxBufSize     = 1000000
)

var sc *bufio.Scanner

func initScanner(r io.Reader) *bufio.Scanner {
	buf := make([]byte, initialBufSize)

	sc := bufio.NewScanner(r)
	sc.Buffer(buf, maxBufSize)
	sc.Split(bufio.ScanWords)
	return sc
}

func main() {
	sc = initScanner(os.Stdin)
	resolve()
}

func resolve() {
	n := scanInt(sc)
	q := scanInt(sc)
	table := newDebugNodeSlice(200001)
	for i := 0; i < n; i++ {
		table.l[i].parent = &table.l[i+1]
		table.l[i+1].left = &table.l[i]
		table.l[i].update()
		table.l[i+1].update()
	}
	var root *SplayTreeNode = &table.l[n]
	for i := 0; i < n; i++ {
		table.l[i].value = scanInt(sc)
		table.l[i].update()
	}
	table.l[n].update()
	for i := 0; i < q; i++ {
		switch scanInt(sc) {
		case 0:
			root = shift(root, scanInt(sc), scanInt(sc))
		case 1:
			l := scanInt(sc)
			r := scanInt(sc)
			tmp, rRoot := root.Split(r + 1)
			lRoot, cRoot := tmp.Split(l)
			fmt.Println(cRoot.minimum)
			root = mergeSplayNode(mergeSplayNode(lRoot, cRoot), rRoot)
		case 2:
			root = root.Get(scanInt(sc))
			root.value = scanInt(sc)
			root.update()
		}
	}
}


C++: #define NDEBUG 1
#include <bits/stdc++.h>

using key_type = int;

enum { L, R };
struct avl_node {
    key_type key;
    std::array<avl_node*, 2> ch;
    int size;
    int height;
    int min;

    static avl_node* const nil;

    avl_node() : avl_node(-1) { }
    avl_node(key_type key) : avl_node(key, nil, nil, 1, 1, key) { }
    avl_node(const key_type key, avl_node *left, avl_node *right, int size, int height, key_type min)
        : key(key), ch({{left, right}}), size(size), height(height), min(min) { }

    void *operator new(size_t) {
        static int p = 0;
        static avl_node pool[400010];
        return pool + p++;
    }
};

avl_node *const avl_node::nil = new avl_node(key_type(), nullptr, nullptr, 0, 0, 1e9);
avl_node *const nil = avl_node::nil;
namespace trush { auto ___ = []() { return nil->ch = {{nil, nil}}; }; };

using np = avl_node*;
using cnp = const avl_node*;

// ok
np update(np n) {
    n->size = n->ch[L]->size + 1 + n->ch[R]->size;
    n->height = std::max(n->ch[L]->height, n->ch[R]->height) + 1;
    n->min = std::min({n->ch[L]->min, n->key, n->ch[R]->min});
    return n;
}

// ok
template <int dir>
np rotate(np n) {
    assert(n->ch[!dir] != nil);
    np root = n->ch[!dir];
    n->ch[!dir] = root->ch[dir];
    root->ch[dir] = n;
    update(n);
    update(root);
    return root;
}

const int B = 50;

// ok
int bfactor(np n) {
    assert(n != nil);
    return n->ch[R]->height - n->ch[L]->height;
}

// ok
np balance(np n) {
    assert(abs(bfactor(n)) <= 2);
    if (bfactor(n) == +B) {
        if (bfactor(n->ch[R]) < 0) n->ch[R] = rotate<R>(n->ch[R]);
        return rotate<L>(n);
    } else if (bfactor(n) == -B) {
        if (bfactor(n->ch[L]) > 0) n->ch[L] = rotate<L>(n->ch[L]);
        return rotate<R>(n);
    } else {
        return n;
    }
}

// ok
np insert_at(np n, int k, key_type x) {
    assert(0 <= k && k <= n->size);
    if (n == nil) return new avl_node(x);
    int sl = n->ch[L]->size;
    if (k <= sl) n->ch[L] = insert_at(n->ch[L], k, x);
    else n->ch[R] = insert_at(n->ch[R], k - sl - 1, x);
    return balance(update(n));
}

// ok
template <int dir>
std::pair<np, np> remove_most(np n) {
    assert(n != nil);
    if (n->ch[dir] != nil) {
        np most;
        std::tie(n->ch[dir], most) = remove_most<dir>(n->ch[dir]);
        return {balance(update(n)), most};
    } else {
        np res = n->ch[!dir];
        n->ch[!dir] = nil;
        return {res, update(n)};
    }
}

// ok
std::pair<np, key_type> remove_at(np n, int k) {
    assert(n != nil);
    int sl = n->ch[L]->size;
    if (k < sl) {
        key_type most;
        std::tie(n->ch[L], most) = remove_at(n->ch[L], k);
        return {balance(update(n)), most};
    } if (k == sl) {
        if (n->ch[R] == nil) {
            return {n->ch[L], n->key};
        } else {
            np most;
            std::tie(n->ch[R], most) = remove_most<L>(n->ch[R]);
            most->ch = n->ch;
            // delete n;
            return {balance(update(most)), n->key};
        }
    } else {
        key_type most;
        std::tie(n->ch[R], most) = remove_at(n->ch[R], k - sl - 1);
        return {balance(update(n)), most};
    }
}

// ok
template <typename Iterator>
np build(Iterator left, Iterator right) {
    int n = right - left;
    Iterator mid = left + n / 2;
    if (n == 0) return nil;
    np l = build(left, mid);
    np r = build(mid + 1, right);
    np m = new avl_node(*mid);
    m->ch = {{l, r}};
    return update(m);
}

void update_at(np n, int k, key_type x) {
    assert(0 <= k && k < n->size);
    int sl = n->ch[L]->size;
    if (k < sl) update_at(n->ch[L], k, x);
    else if (k == sl) n->key = x;
    else update_at(n->ch[R], k - sl - 1, x);
    update(n);
}

key_type range_min(np n, int l, int r) {
    assert(n != nil);
    assert(0 <= l && l <= r);
    assert(l <= r && r <= n->size);
    if (l == 0 && r == n->size) return n->min;
    int sl = n->ch[L]->size;
    key_type res = 1e9;
    if (l < sl) res = std::min(res, range_min(n->ch[L], l, std::min(r, sl)));
    if (l <= sl && sl < r) res = std::min(res, n->key);
    if (sl + 1 < r) res = std::min(res, range_min(n->ch[R], std::max(0, l - sl - 1), r - sl - 1));
    return res;
}

using namespace std;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    int n, q;
    cin >> n >> q;
    vector<int> a(n);
    for (int i = 0; i < n; ++i) cin >> a[i];
    np root = build(a.begin(), a.end());
    for (int i = 0; i < q; ++i) {
        int t, x, y;
        cin >> t >> x >> y;
        if (t == 0) {
            int t;
            tie(root, t) = remove_at(root, y);
            root = insert_at(root, x, t);
        } else if (t == 1) {
            ++y;
            cout << range_min(root, x, y) << '\n';
        } else {
            update_at(root, x, y);
        }
    }
}