Problem:
Score : 700 points

Problem Statement

There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.

You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.

Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 10^9(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.

Sample Input 1

4
0
1
1
2

Sample Output 1

3

We can make X equal to A as follows:

Choose i=2. X becomes (0,0,1,0).

Choose i=1. X becomes (0,1,1,0).

Choose i=3. X becomes (0,1,1,2).

Sample Input 2

3
1
2
1

Sample Output 2

-1

Sample Input 3

9
0
1
1
0
1
2
2
1
2

Sample Output 3

8

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

import java.io.DataInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;


public class Main {
	
	public static void main(String[] args) throws IOException {
		Main m = new Main();
		//*
		m.input();
		m.solve();
		m.output();
		/*/
		m.debug();
		//*/
	}
	
	public void debug() {
	}
	
	InputUtil in = new InputUtil();
	PrintWriter out = new PrintWriter(System.out);
	
	int N;
	int[] A;
	long ans = -1;
//	boolean ans = false;
			
	public void input() throws IOException {
		N = in.nextInt();
		A = in.nextInt(new int[N]);
	}
	
	public void solve() throws IOException {
		int count = 0;
		if (A[0] != 0) return;
		for (int i=1; i<N; i++) {
			if (A[i-1]+1<A[i]) {
				return;
			} else if (A[i-1]>=A[i]) {
				count += A[i-1];
			}
		}
		count += A[N-1];
		ans = count;
	}
	
	
	
	public void output() {
		out.println(ans);
		out.flush();
	}
}

class Group {
	public Group(int groupNo) {
		this.groupNo=groupNo;
	}
	Group parent = null;
	int groupNo = -1;

	public Group getRootGroup() {
		if (this.parent != null) {
			return this.parent = this.parent.getRootGroup();
		} else {
			return this;
		}
	}
	
	public void setParentGroup(Group parent) {
		Group root = parent.getRootGroup();
		if (this.parent != null) {
			this.parent.setParentGroup(root);
		}
		this.parent = root;
	}
	
	public int getGroupNo() {
		return getRootGroup().groupNo;
	}
	public String toString() {
		return Integer.toString(getGroupNo());
	}
}

class InputUtil {
	//Static Fields
	private static final int BUFSIZ = 100000;
	boolean lineMode = false;
	
	//Fields
	protected InputStream in;
	private byte[] buf = null;
	private int ptr = 0;
	private int max = -1;
	private DataInputStream dis = null;
	//Constructors
	public InputUtil() {this(System.in,BUFSIZ);}
	public InputUtil(InputStream in, int bufsiz) {
		initBuf(bufsiz);
		initIn(in);
	}
	
	//Methods
	//Initializer
	protected void initIn(InputStream in) {dis = new DataInputStream(this.in = in);}
	protected void initBuf(int bufsiz) {buf = new byte[bufsiz];}
	
	//buffer operation
	private void next() throws IOException {ptr++; readBuf();}
	private void readBuf() throws IOException {
		if(ptr >= max && dis.available()>0) {
			if(max>0) Arrays.fill(buf,0,max,(byte)0);
			max = dis.read(buf);
			ptr = 0;
		}
	}
	
	
	//String Input Reader/Parser
	private boolean isCrLf(byte b) {return b == 0x0a || b == 0x0d; }
	
	private void skipOneCrLf() throws IOException {
		byte b = buf[ptr];
		if (isCrLf(b)) {
			ptr++;
			if (b == 0x0d) {
				readBuf();
				if (ptr < max && buf[ptr] == 0x0a) {
					ptr++;
				}
			}
		}
	}
	
	public String nextLine() throws IOException {
		StringBuilder sb = new StringBuilder();
		boolean isFirst = true;
		for(readBuf(); ptr < max ;readBuf()) {
			byte b = buf[ptr];
			if(isCrLf(b)) {
				skipOneCrLf();
				if (!isFirst || lineMode) {
					break;
				}
			}else{
				int strPtr = ptr++;
				int endPtr = -1;
				for(int i = ptr; i<max; i++) {
					if(isCrLf(buf[i])) {
						endPtr = i;
						break;
					}
				}
				if(endPtr == -1) endPtr = max;
				sb.append(new String(buf,strPtr,endPtr-strPtr,"UTF-8"));
				ptr = endPtr;
			}
			isFirst = false;
		}
		lineMode = true;
		return sb.toString();
	}
	
	public byte nextByte() throws IOException {
		lineMode=false;
		readBuf();
		if(ptr < max) {
			return buf[ptr++];
		}else{
			return -1;
		}
	}
	
	//Number Input Reader/Parser
	private boolean isNum(byte b) {return '0' <= b && b <= '9'; }
	private boolean isMinus(byte b) {return b=='-'; }
	
	public int nextInt() throws IOException {
		lineMode=false;
		readBuf();
		return (int)_nextLong();
	}
	
	public int[] nextInt(int[] result) throws IOException {
		lineMode=false;
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = (int)_nextLong();
		}
		return result;
	}
	
	private long _nextLong() throws IOException {
		int sign = 1;
		long res = 0;
		byte c;
		while (!isNum(c=buf[ptr]) && !isMinus(c)) 
			next();
		if (isMinus(buf[ptr])) {
			sign = -1;
			next();
		}
		while (isNum(c=buf[ptr])) {
			res *= 10;
			res += c - '0' ;
			next();
		}
		next();
		return sign * res;
	}
	
	public long nextLong() throws IOException {
		lineMode=false;
		readBuf();
		return _nextLong();
	}
	
	public long[] nextLong(long[] result) throws IOException {
		lineMode=false;
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = _nextLong();
		}
		return result;
	}
	
	//Close 
	public void close() throws IOException {
		if(!this.in.equals(System.in)) 
			this.in.close();
	}

}

class OutputUtil {
	public static final String EOF = System.lineSeparator();

	public static void outputDivSpace(PrintWriter out, int[] a) {
		OutputUtil.output(out,a,0,a.length," ");
	}
	
	public static void outputDivEOF(PrintWriter out, int[] a) {
		OutputUtil.output(out,a,0,a.length,EOF);
	}
	
	public static void output(PrintWriter out, int[] a, int off, int len, String delim) {
		out.print(a[off]);
		for(int i=off+1; i<len; i++){
			out.print(delim);
			out.print(a[i]);
		}
		out.println("");
		out.flush();
	}
}