Problem: In a far away galaxy there is war again. The treacherous Republic made k precision strikes of power ai on the Empire possessions. To cope with the republican threat, the Supreme Council decided to deal a decisive blow to the enemy forces. 

To successfully complete the conflict, the confrontation balance after the blow should be a positive integer. The balance of confrontation is a number that looks like <image>, where p = n! (n is the power of the Imperial strike), <image>. After many years of war the Empire's resources are low. So to reduce the costs, n should be a minimum positive integer that is approved by the commanders.

Help the Empire, find the minimum positive integer n, where the described fraction is a positive integer.

Input

The first line contains integer k (1 ≤ k ≤ 106). The second line contains k integers a1, a2, ..., ak (1 ≤ ai ≤ 107).

Output

Print the minimum positive integer n, needed for the Empire to win.

Please, do not use the %lld to read or write 64-but integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

2
1000 1000


Output

2000

Input

1
2


Output

2

Solution (in JAVA):

Solution:
//package round181;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class E {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int[] primes = sieveEratosthenes(10000000);
		
		int K = ni();
		int[] a = na(K);
		long[] es = new long[700000];
		a = radixSort(a);
		for(int i = 0;i < K;i++){
			a[i] *= 2;
		}
//		long A = System.currentTimeMillis();
		for(int i = 0;i < primes.length;i++){
			int p = primes[i];
			for(int j = 0;j < K;){
				int f = a[j]/2/p;
				int ind = Arrays.binarySearch(a, 2*(f+1)*p-1);
				ind = -ind-1;
				long g = 0;
				for(int u = f;u > 0;u /= p){
					g += u;
				}
				es[i] += g*(ind-j);
//				es[i] += f*(ind-j);
				j = ind;
			}
//			if(es[i] > 0)tr(i, es[i]);
		}
//		for(int i = 0;i < primes.length;i++){
//			int p = primes[i];
//			for(long m = p;m*2 <= a[K-1];m *= p){
//				for(int j = 0;j < K;){
//					int f = (int)(a[j]/2/m);
//					int ind = Arrays.binarySearch(a, (int)(2*(f+1)*m)-1);
//					ind = -ind-1;
//					es[i]+=(long)f*(ind-j);
//					j = ind;
//				}
//			}
////			if(es[i] > 0)tr(i, es[i]);
//		}
//		long B = System.currentTimeMillis();
//		tr(B-A);
		long cmax = 0;
		long ret = 1;
		for(int i = primes.length-1;i >= 0;i--){
			if(es[i] > cmax){
				cmax = es[i];
				//(primes[i]*?)
				long low = 0, high = es[i]+1;
				while(high - low > 1){
					long x = (high + low) / 2;
					long esum = 0;
					for(long y = x;y > 0;y /= primes[i]){
						esum += y;
					}
					if(esum >= es[i]){
						high = x;
					}else{
						low = x;
					}
				}
				
				ret = Math.max(ret, high * (long)primes[i]);
			}
		}
		out.println(ret);
	}
	
	public static int[] radixSort(int[] f)
	{
		int[] to = new int[f.length];
		{
			int[] b = new int[65537];
			for(int i = 0;i < f.length;i++)b[1+(f[i]&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < f.length;i++)to[b[f[i]&0xffff]++] = f[i];
			int[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < f.length;i++)b[1+(f[i]>>>16)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < f.length;i++)to[b[f[i]>>>16]++] = f[i];
			int[] d = f; f = to;to = d;
		}
		return f;
	}
	
	public static int[] sieveEratosthenes(int n) {
		if(n <= 32){
			int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
			for(int i = 0;i < primes.length;i++){
				if(n < primes[i]){
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
		for(int tp : tprimes){
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for(int i = (tp - 3) / 2;i < tp << 5;i += tp)
				ptn[i >> 5] |= 1 << (i & 31);
			for(int i = 0;i < tp;i++){
				for(int j = i;j < sup;j += tp)
					isp[j] |= ptn[i];
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4,
				13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 };
		int h = n / 2;
		for(int i = 0;i < sup;i++){
			for(int j = ~isp[i];j != 0;j &= j - 1){
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if(p > n)
					break;
				ret[pos++] = p;
				for(int q = pp;q <= h;q += p)
					isp[q >> 5] |= 1 << (q & 31);
			}
		}

		return Arrays.copyOf(ret, pos);
	}
	
	void run() throws Exception
	{
//		int n = 1000000, m = 99999;
//		Random gen = new Random(1);
//		StringBuilder sb = new StringBuilder();
//		sb.append(n + " ");
//		for(int i = 0;i < n;i++){
//			sb.append(gen.nextInt(10000000)+1 + " ");
//		}
//		INPUT = sb.toString();
		
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}