Problem: You are given an array a_0, a_1, ..., a_{N-1} of length N. Process Q queries of the following types.

The type of i-th query is represented by T_i.

* T_i=1: You are given two integers X_i,V_i. Replace the value of A_{X_i} with V_i.
* T_i=2: You are given two integers L_i,R_i. Calculate the maximum value among A_{L_i},A_{L_i+1},\cdots,A_{R_i}.
* T_i=3: You are given two integers X_i,V_i. Calculate the minimum j such that X_i \leq j \leq N, V_i \leq A_j. If there is no such j, answer j=N+1 instead.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 0 \leq A_i \leq 10^9
* 1 \leq Q \leq 2 \times 10^5
* 1 \leq T_i \leq 3
* 1 \leq X_i \leq N, 0 \leq V_i \leq 10^9 (T_i=1,3)
* 1 \leq L_i \leq R_i \leq N (T_i=2)
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N Q
A_1 A_2 \cdots A_N
First query
Second query
\vdots
Q-th query


Each query is given in the following format:

If T_i=1,3,


T_i X_i V_i


If T_i=2,


T_i L_i R_i


Output

For each query with T_i=2, 3, print the answer.

Example

Input

5 5
1 2 3 2 1
2 1 5
3 2 3
1 3 1
2 2 4
3 1 3


Output

3
3
2
6

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;

public class Main {
    static FastScanner sc = new FastScanner(System.in);
    static StringBuilder sb = new StringBuilder();
    static PrintWriter pw = new PrintWriter(System.out);

    public static void main(String[] args) {
        final int N = sc.nextInt();
        final int Q = sc.nextInt();
        final var A = new Integer[N];
        Arrays.setAll(A, i -> sc.nextInt());
        for (int l = 0, r = N - 1; l < r; l++, r--) {
            var tmp = A[l]; A[l] = A[r]; A[r] = tmp;
        }
        var t = new SegTree<Integer>(A, Integer::max, -1);
        for (int $ = 0; $ < Q; $++) {
            int query = sc.nextInt();
            if (query == 1) {
                int p = N - sc.nextInt();
                int v = sc.nextInt();
                t.set(p, v);
            } else if (query == 2) {
                int r = N - sc.nextInt() + 1;
                int l = N - sc.nextInt();
                sb.append(t.prod(l, r)).append('\n');
            } else {
                int p = N - sc.nextInt() + 1;
                int v = sc.nextInt();
                sb.append(N - t.minLeft(p, x -> x < v) + 1).append('\n');
            }
        }
        pw.write(sb.toString());
        pw.flush();
        pw.close();
    }
 
    /**
     * @unverified {@link SegTree#minLeft}
     * 
     * @verified https://atcoder.jp/contests/practice2/tasks/practice2_j
     */
    static class SegTree<S> {
        final int MAX;

        final int N;
        final java.util.function.BinaryOperator<S> Op;
        final S E;

        final S[] Dat;

        @SuppressWarnings("unchecked")
        public SegTree(int n, java.util.function.BinaryOperator<S> op, S e) {
            this.MAX = n;
            int k = 1;
            while (k < n) k <<= 1;
            this.N = k;
            this.E = e;
            this.Op = op;
            this.Dat = (S[]) new Object[N << 1];
            java.util.Arrays.fill(Dat, E);
        }

        public SegTree(S[] dat, java.util.function.BinaryOperator<S> op, S e) {
            this(dat.length, op, e);
            build(dat);
        }

        private void build(S[] dat) {
            int l = dat.length;
            System.arraycopy(dat, 0, Dat, N, l);
            for (int i = N - 1; i > 0; i--) {
                Dat[i] = Op.apply(Dat[i << 1 | 0], Dat[i << 1 | 1]);
            }
        }

        public void set(int p, S x) {
            exclusiveRangeCheck(p);
            Dat[p += N] = x;
            p >>= 1;
            while (p > 0) {
                Dat[p] = Op.apply(Dat[p << 1 | 0], Dat[p << 1 | 1]);
                p >>= 1;
            }
        }

        public S get(int p) {
            exclusiveRangeCheck(p);
            return Dat[p + N];
        }

        public S prod(int l, int r) {
            if (l > r) {
                throw new IllegalArgumentException(
                    String.format("Invalid range: [%d, %d)", l, r)
                );
            }
            inclusiveRangeCheck(l);
            inclusiveRangeCheck(r);
            S sumLeft = E;
            S sumRight = E;
            l += N; r += N;
            while (l < r) {
                if ((l & 1) == 1) sumLeft = Op.apply(sumLeft, Dat[l++]);
                if ((r & 1) == 1) sumRight = Op.apply(Dat[--r], sumRight);
                l >>= 1; r >>= 1;
            }
            return Op.apply(sumLeft, sumRight);
        }

        public S allProd() {
            return Dat[1];
        }

        public int maxRight(int l, java.util.function.Predicate<S> f) {
            inclusiveRangeCheck(l);
            if (!f.test(E)) {
                throw new IllegalArgumentException("Identity element must satisfy the condition.");
            }
            if (l == MAX) return MAX;
            l += N;
            S sum = E;
            do {
                l >>= Integer.numberOfTrailingZeros(l);
                if (!f.test(Op.apply(sum, Dat[l]))) {
                    while (l < N) {
                        l = l << 1;
                        if (f.test(Op.apply(sum, Dat[l]))) {
                            sum = Op.apply(sum, Dat[l]);
                            l++;
                        }
                    }
                    return l - N;
                }
                sum = Op.apply(sum, Dat[l]);
                l++;
            } while ((l & -l) != l);
            return MAX;
        }

        public int minLeft(int r, java.util.function.Predicate<S> f) {
            inclusiveRangeCheck(r);
            if (!f.test(E)) {
                throw new IllegalArgumentException("Identity element must satisfy the condition.");
            }
            if (r == 0) return 0;
            r += N;
            S sum = E;
            do {
                r--;
                while (r > 1 && (r & 1) == 1) r >>= 1;
                if (!f.test(Op.apply(Dat[r], sum))) {
                    while (r < N) {
                        r = r << 1 | 1;
                        if (f.test(Op.apply(Dat[r], sum))) {
                            sum = Op.apply(Dat[r], sum);
                            r--;
                        }
                    }
                    return r + 1 - N;
                }
                sum = Op.apply(Dat[r], sum);
            } while ((r & -r) != r);
            return 0;
        }

        private void exclusiveRangeCheck(int p) {
            if (p < 0 || p >= MAX) {
                throw new IndexOutOfBoundsException(
                    String.format("Index %d is not in [%d, %d).", p, 0, MAX)
                );
            }
        }

        private void inclusiveRangeCheck(int p) {
            if (p < 0 || p > MAX) {
                throw new IndexOutOfBoundsException(
                    String.format("Index %d is not in [%d, %d].", p, 0, MAX)
                );
            }
        }
    }
    
    static class FastScanner {
        private final InputStream in;
        private final byte[] buf = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        public FastScanner(InputStream in) {this.in = in;}
        private boolean hasNextByte() {
            if (ptr < buflen) return true;
            ptr = 0;
            try {buflen = in.read(buf);}
            catch (final IOException e) {e.printStackTrace();}
            return buflen > 0;
        }
        private int readByte() {return hasNextByte() ? buf[ptr++] : -1;}
        public boolean hasNext() {
            while (hasNextByte() && !(33 <= buf[ptr] && buf[ptr] <= 126)) ptr++;
            return hasNextByte();
        }
        private StringBuilder nextSequence() {
            if (!hasNext()) throw new NoSuchElementException();
            final StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
            return sb;
        }
        public String next() {
            return nextSequence().toString();
        }
        public String next(int len) {
            return new String(nextChars(len));
        }
        public char[] nextChars() {
            final StringBuilder sb = nextSequence();
            int l = sb.length();
            char[] dst = new char[l];
            sb.getChars(0, l, dst, 0);
            return dst;
        }
        public char[] nextChars(int len) {
            if (!hasNext()) throw new NoSuchElementException();
            char[] s = new char[len];
            int i = 0;
            int b = readByte();
            while (33 <= b && b <= 126 && i < len) {s[i++] = (char) b; b = readByte();}
            if (i != len) throw new NoSuchElementException(String.format("length %d is longer than the sequence.", len));
            return s;
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {minus = true; b = readByte();}
            if (b < '0' || '9' < b) throw new NumberFormatException();
            while (true) {
                if ('0' <= b && b <= '9') n = n * 10 + b - '0';
                else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
                else throw new NumberFormatException();
                b = readByte();
            }
        }
        public int nextInt() {return Math.toIntExact(nextLong());}
        public double nextDouble() {return Double.parseDouble(next());}
    }

    static int[] nextInts(int n) {
        var dat = new int[n];
        Arrays.setAll(dat, i -> sc.nextInt());
        return dat;
    }

    static long[] nextLongs(int n) {
        var dat = new long[n];
        Arrays.setAll(dat, i -> sc.nextLong());
        return dat;
    }
}