One tradition of welcoming the New Year is launching fireworks into the sky. Usually a launched firework flies vertically upward for some period of time, then explodes, splitting into several parts flying in different directions. Sometimes those parts also explode after some period of time, splitting into even more parts, and so on.

Limak, who lives in an infinite grid, has a single firework. The behaviour of the firework is described with a recursion depth n and a duration for each level of recursion t1, t2, ..., tn. Once Limak launches the firework in some cell, the firework starts moving upward. After covering t1 cells (including the starting cell), it explodes and splits into two parts, each moving in the direction changed by 45 degrees (see the pictures below for clarification). So, one part moves in the top-left direction, while the other one moves in the top-right direction. Each part explodes again after covering t2 cells, splitting into two parts moving in directions again changed by 45 degrees. The process continues till the n-th level of recursion, when all 2n - 1 existing parts explode and disappear without creating new parts. After a few levels of recursion, it's possible that some parts will be at the same place and at the same time — it is allowed and such parts do not crash.

Before launching the firework, Limak must make sure that nobody stands in cells which will be visited at least once by the firework. Can you count the number of those cells?

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 30) — the total depth of the recursion.

The second line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 5). On the i-th level each of 2i - 1 parts will cover ti cells before exploding.

Output

Print one integer, denoting the number of cells which will be visited at least once by any part of the firework.

Examples

Input

4
4 2 2 3


Output

39


Input

6
1 1 1 1 1 3


Output

85


Input

1
3


Output

3

Note

For the first sample, the drawings below show the situation after each level of recursion. Limak launched the firework from the bottom-most red cell. It covered t1 = 4 cells (marked red), exploded and divided into two parts (their further movement is marked green). All explosions are marked with an 'X' character. On the last drawing, there are 4 red, 4 green, 8 orange and 23 pink cells. So, the total number of visited cells is 4 + 4 + 8 + 23 = 39.

<image>

For the second sample, the drawings below show the situation after levels 4, 5 and 6. The middle drawing shows directions of all parts that will move in the next level.

<image>
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class TestClass {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	
	public static class Queue{
		private class node{
			int val;
			node next;
			node(int a){
				val = a;
				next = null;
			}
		}
		node head,tail;
		Queue(){
			head = null;
			tail = null;
		}
		public void EnQueue(int a){
			if(head==null){
				node p = new node(a);
				head = p;
				tail = p;
			}
			else{
				node p = new node(a);
				tail.next = p;
				tail = p;
			}
		}
		public int DeQueue(){
			int a = head.val;
			head = head.next;
			return a;
		}
		public boolean isEmpty(){
			return head==null;
		}
	}
	public static long pow(long x,long y,long m){
		if(y==0)
    		return 1;
    	long k = pow(x,y/2,m);
    	if(y%2==0)
    		return (k*k)%m;
    	else
    		return (((k*k)%m)*x)%m;
    }
	static long Inversex = 0,Inversey = 0;
	public static void InverseModulo(long a,long m){
		if(m==0){
			Inversex = 1;
			Inversey = 0;
		}
		else{
    		InverseModulo(m,a%m);
    		long temp = Inversex;
    		Inversex = Inversey;
    		Inversey = temp+ - (a/m)*Inversey;
    	}
    }
    static long mod1 = 1000000007;
    static long mod2 = 1000000009;
	public static long gcd(long a,long b){
		if(a%b==0)
			return b;
		return gcd(b,a%b);
	}
	public static boolean isPrime(long a){
		if(a==1)
			return false;
		else if(a==2||a==3)
			return true;
		for(long i=2;i<=Math.sqrt(a);i++)
			if(a%i==0)
				return false;
		return true;
	}
	public static double distance(int a,int b,int x,int y){
		return Math.sqrt(((long)(a-x)*(long)(a-x))+((long)(b-y)*(long)(b-y)));
	}
	public static class Pair implements Comparable<Pair> {
		long u;
		long v;
		BigInteger bi;
		public Pair(long u, long v) {
			this.u = u;
			this.v = v;
		}
		public int hashCode() {
			int hu = (int) (u ^ (u >>> 32));
			int hv = (int) (v ^ (v >>> 32));
			return 31 * hu + hv;
		}
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return u == other.u && v == other.v;
		}
		public int compareTo(Pair other) {
			return Long.compare(u, other.u) != 0 ? Long.compare(u, other.u) : Long.compare(v, other.v);
		}
		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	public static int seive(int a[],boolean b[],TreeSet<Integer> c){
		int count = 0;
		for(int i=2;i<a.length;i++){
			if(!b[i]){
				for(int j=i*i;j<a.length&&j>0;j=j+i)
					b[j] = true;
				c.add(i);
				a[count++] = i;
			}
		}
		return count;
	}
	public static void MatrixMultiplication(int a[][],int b[][],int c[][]){
		for(int i=0;i<a.length;i++){
			for(int j=0;j<b[0].length;j++){
				c[i][j] = 0;
				for(int k=0;k<b.length;k++)
					c[i][j]=(int)((c[i][j]+((a[i][k]*(long)b[k][j])%mod1))%mod1);
			}
		}
	}
	public static void Equal(int arr[][],int temp[][]){
		for(int i=0;i<arr.length;i++){
			for(int j=0;j<arr.length;j++)
				temp[i][j] = arr[i][j];
		}
	}
	public static class Trie {
		Node head;
		private class Node{
			Node a[] = new Node[2];
			boolean val;
			Node(){
				a[0] = null;
				a[1] = null;
				val = false;
			}
		}
		Trie(){
			head = new Node();
		}
		public void insert(Stack<Integer> s){
			Node temp = head;
			while(!s.isEmpty()){
				int q = s.pop();
				if(temp.a[q]==null)
					temp.a[q] = new Node();
				temp = temp.a[q];
			}
			temp.val = true;
		}
		public Node delete(Stack<Integer> s,Node temp){
			if(s.isEmpty())
				return null;
			int q = s.pop();
			temp.a[q] = delete(s,temp.a[q]);
			if(temp.a[q]==null&&temp.a[q^1]==null)
				return null;
			else
				return temp;
		}
		public void get(Stack<Integer> s,Stack<Integer> p){
			Node temp = head;
			while(!p.isEmpty()){
				int q = p.pop();
				if(temp.a[q]!=null){
					s.push(q);
					temp = temp.a[q];
				}
				else{
					s.push(q^1);
					temp = temp.a[q^1];
				}
			}
		}
	}
	public static void Merge(long a[][],int p,int r){
        if(p<r){
            int q = (p+r)/2;
            Merge(a,p,q);
            Merge(a,q+1,r);
            Merge_Array(a,p,q,r);
        }
    }
	public static void get(long a[][],long b[][],int i,int j){
		for(int k=0;k<a[i].length;k++)
			a[i][k] = b[j][k];
	}
    public static void Merge_Array(long a[][],int p,int q,int r){
        long b[][] = new long[q-p+1][a[0].length];
        long c[][] = new long[r-q][a[0].length];
        for(int i=0;i<b.length;i++){
            get(b,a,i,p+i);
        }
        for(int i=0;i<c.length;i++){
            get(c,a,i,q+i+1);
        }
        int i = 0,j = 0;
        for(int k=p;k<=r;k++){
            if(i==b.length){
                get(a,c,k,j);
                j++;
            }
            else if(j==c.length){
                get(a,b,k,i);
                i++;
            }
            else if(b[i][0]<c[j][0]){
                get(a,b,k,i);
                i++;
            }
            else{
                get(a,c,k,j);
                j++;
            }
        }
    }
    static boolean include[][] = new boolean[400][400];
    static boolean visited[][][][] = new boolean[400][400][8][30];
    public static void fun(Pair state[],int a[],int p,int q,int r,int s){
    	if(s==a.length)
    		return ;
    	if(visited[p][q][r][s])
    		return ;
    	visited[p][q][r][s] = true;
    	int nm = a[s];
    	for(int i=0;i<nm;i++)
    		include[p+(int)(state[r].u*i)][q+(int)(state[r].v*i)] = true;
    	fun(state,a,(int)(p+state[r].u*(nm-1)+state[(r+1)%8].u),(int)(q+state[r].v*(nm-1)+state[(r+1)%8].v),(r+1)%8,s+1);
    	fun(state,a,(int)(p+state[r].u*(nm-1)+state[(r+7)%8].u),(int)(q+state[r].v*(nm-1)+state[(r+7)%8].v),(r+7)%8,s+1);
    }
	private static void soln(){
		Pair state[] = new Pair[8];
		state[0] = new Pair(0,1);
		state[1] = new Pair(1,1);
		state[2] = new Pair(1,0);
		state[3] = new Pair(1,-1);
		state[4] = new Pair(0,-1);
		state[5] = new Pair(-1,-1);
		state[6] = new Pair(-1,0);
		state[7] = new Pair(-1,1);
		int n = nI();
		int a[] = new int[n];
		for(int i=0;i<n;i++)
			a[i] = nI();
		fun(state,a,200,200,0,0);
		int count = 0;
		for(int i=0;i<400;i++){
			for(int j=0;j<400;j++)
				if(include[i][j])
					count++;
		}
		pw.println(count);
	}
	public static void main(String[] args) {
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		soln();
		pw.close();
	}
	// To Get Input
	// Some Buffer Methods
	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}
	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}
	private static int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
	private static int nI() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	private static long nL() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
	private static String nLi() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}
	private static int[] nIA(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
			arr[i] = nI();
		return arr;
	}
	private static long[] nLA(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++)
			arr[i] = nL();
		return arr;
	}
	private static void pArray(int[] arr) {
		for (int i = 0; i < arr.length; i++)
			pw.print(arr[i] + " ");
		pw.println();
		return;
	}
	private static void pArray(long[] arr) {
		for (int i = 0; i < arr.length; i++)
			pw.print(arr[i] + " ");
		pw.println();
		return;
	}
	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}