Problem:
Score : 400 points

Problem Statement

We have N bricks arranged in a row from left to right.

The i-th brick from the left (1 \leq i \leq N) has an integer a_i written on it.

Among them, you can break at most N-1 bricks of your choice.

Let us say there are K bricks remaining. Snuke will be satisfied if, for each integer i (1 \leq i \leq K), the i-th of those brick from the left has the integer i written on it.

Find the minimum number of bricks you need to break to satisfy Snuke's desire. If his desire is unsatisfiable, print -1 instead.

Constraints

All values in input are integers.

1 \leq N \leq 200000

1 \leq a_i \leq N

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum number of bricks that need to be broken to satisfy Snuke's desire, or print -1 if his desire is unsatisfiable.

Sample Input 1

3
2 1 2

Sample Output 1

1

If we break the leftmost brick, the remaining bricks have integers 1 and 2 written on them from left to right, in which case Snuke will be satisfied.

Sample Input 2

3
2 2 2

Sample Output 2

-1

In this case, there is no way to break some of the bricks to satisfy Snuke's desire.

Sample Input 3

10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

7

Sample Input 4

1
1

Sample Output 4

0

There may be no need to break the bricks at all.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.util.StringJoiner;

class Main {

    static PrintWriter out;
    static InputReader sc;

    public static void main(String[] args) {
        sc = new InputReader(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    static void solve() {
        int N = sc.nextInt();
        int[] a = sc.nextIntArray(N);
        int[] b = new int[N];
        for (int i = 0; i < N; i++) {
            b[i] = (i + 1) - a[i];
        }
        int cnt = 0;
        for (int i = 0; i < N; i++) {
            if (b[i] - cnt < 0) {
                cnt++;
            } else if (b[i] - cnt > 0) {
                cnt += b[i] - cnt;
            }
        }
        if (cnt > N - 1) {
            out.println(-1);
            return;
        }
        out.println(cnt);
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            Class<?> type = arg.getClass();
            if (!type.isArray()) {
                j.add(arg.toString());
            } else if (type.getComponentType().isArray()) {
                for (Object o : (Object[]) arg) {
                    debug(o);
                }
            } else if (arg instanceof int[]) {
                j.add(Arrays.toString((int[]) arg));
            } else if (arg instanceof long[]) {
                j.add(Arrays.toString((long[]) arg));
            } else if (arg instanceof double[]) {
                j.add(Arrays.toString((double[]) arg));
            } else if (arg instanceof char[]) {
                j.add(Arrays.toString((char[]) arg));
            } else if (arg instanceof boolean[]) {
                j.add(Arrays.toString((boolean[]) arg));
            } else if (arg instanceof Object[]) {
                j.add(Arrays.toString((Object[]) arg));
            } else {
                j.add(arg.toString());
            }
        }
        System.err.println(j.toString());
    }

    static class InputReader {

        private InputStream in;
        private byte[] buffer = new byte[1024];
        private int curbuf;
        private int lenbuf;

        public InputReader(InputStream in) {
            this.in = in;
            this.curbuf = this.lenbuf = 0;
        }

        public boolean hasNextByte() {
            if (this.curbuf >= this.lenbuf) {
                this.curbuf = 0;
                try {
                    this.lenbuf = this.in.read(this.buffer);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (this.lenbuf <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (this.hasNextByte()) {
                return this.buffer[this.curbuf++];
            } else {
                return -1;
            }
        }

        private boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private void skip() {
            while (this.hasNextByte() && this.isSpaceChar(this.buffer[this.curbuf])) {
                this.curbuf++;
            }
        }

        public boolean hasNext() {
            this.skip();
            return this.hasNextByte();
        }

        public String next() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            StringBuilder sb = new StringBuilder();
            int b = this.readByte();
            while (!this.isSpaceChar(b)) {
                sb.appendCodePoint(b);
                b = this.readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            int c = this.readByte();
            while (this.isSpaceChar(c)) {
                c = this.readByte();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = this.readByte();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = this.readByte();
            } while (!this.isSpaceChar(c));
            return minus ? -res : res;
        }

        public long nextLong() {
            if (!this.hasNext()) {
                throw new NoSuchElementException();
            }
            int c = this.readByte();
            while (this.isSpaceChar(c)) {
                c = this.readByte();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = this.readByte();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = res * 10 + c - '0';
                c = this.readByte();
            } while (!this.isSpaceChar(c));
            return minus ? -res : res;
        }

        public double nextDouble() {
            return Double.parseDouble(this.next());
        }

        public int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = this.nextInt();
            }
            return a;
        }

        public long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = this.nextLong();
            }
            return a;
        }

        public char[][] nextCharMap(int n, int m) {
            char[][] map = new char[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = this.next().toCharArray();
            }
            return map;
        }
    }
}