// Problem: 840_C. On the Bench
// Time complexity: cubic
//package round429;
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 C2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] a = na(n);
		for(int i = 0;i < n;i++){
			int v = a[i];
			for(int j = 2;j*j <= v;j++){
				while(v % (j*j) == 0){
					v /= j*j;
				}
			}
			a[i] = v;
		}
		
		Arrays.sort(a);
		int[] f = new int[n];
		int p = 0;
		for(int i= 0;i < n;i++){
			if(i > 0 && a[i] != a[i-1]){
				p++;
			}
			f[p]++;
		}
		f = Arrays.copyOf(f, p+1);
		int mod = 1000000007;
		
		int[][] fif = enumFIF(1000, mod);
		long[] res = countSameNeighborsSequence(f, fif, mod);
		long ans = res[0];
		for(int v : f){
			ans = ans * fif[0][v] % mod;
		}
		
		out.println(ans);
	}
	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	public static long[] countSameNeighborsSequence(int[] a, int[][] fif, int mod)
	{
		int n = a.length;
		
		int bef = a[0];
		int aft = a[0];
		long[] dp = new long[bef];
		dp[bef-1] = 1;
		for(int u = 1;u < n;u++){
			int v = a[u];
			aft += v;
			long[][] ldp = new long[bef][aft];
			for(int i = 0;i < dp.length;i++){
				ldp[i][0] = dp[i];
			}
			
			for(int i = 0;i < v;i++){
				long[][] ndp = new long[bef][aft];
				for(int j = 0;j < bef;j++){
					for(int k = 0;j+k < aft;k++){
						if(ldp[j][k] == 0)continue;
						// XX -> XCX
						if(j > 0){
							ndp[j-1][k] += ldp[j][k] * j;
							ndp[j-1][k] %= mod;
						}
						
						// CC -> CCC
						if(k > 0){
							ndp[j][k+1] += ldp[j][k] * k;
							ndp[j][k+1] %= mod;
						}
						
						// XC -> XCC
						// #XC = 2*(i-k)
						if(2*(i-k) > 0){
							ndp[j][k+1] += ldp[j][k] * (2*(i-k));
							ndp[j][k+1] %= mod;
						}
						
						// XY -> XCY
						// #XY = bef+i+1-#XC-#CC-#XX
						if(bef+i+1-j-k-2*(i-k) > 0){
							ndp[j][k] += ldp[j][k] * (bef+i+1-j-k-2*(i-k));
							ndp[j][k] %= mod;
						}
					}
				}
				ldp = ndp;
			}
			
			dp = new long[aft];
			for(int j = 0;j < bef;j++){
				for(int k = 0;j+k < aft;k++){
					dp[j+k] += ldp[j][k];
					if(dp[j+k] >= mod)dp[j+k] -= mod;
				}
			}
			for(int j = 0;j < aft;j++)dp[j] = dp[j] * fif[1][v] % mod;
			bef = aft;
		}
		return dp;
	}
	
	void run() throws Exception
	{
		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 C2().run(); }
	
	private byte[] inbuf = new byte[1024];
	public 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)); }
}