source_code: import java.io.*;
  import java.util.*;
  
  public class C {
  
  	int removeSq(int x) {
  		for (int i = 2; i * i <= x; i++) {
  			while (x % (i * i) == 0) {
  				x /= i * i;
  			}
  		}
  		return x;
  	}
  	
  	void submit() {
  		int n = nextInt();
  		HashMap<Integer, Integer> map = new HashMap<>();
  		for (int i = 0; i < n; i++) {
  			int x = removeSq(nextInt());
  			map.merge(x, 1, Integer::sum);
  		}
  		
  		int[] a = new int[map.size()];
  		int ptr = 0;
  		for (Integer x : map.values()) {
  			a[ptr++] = x;
  		}
  
  		int ret = go(a);
  		for (int x : a) {
  			ret = (int)((long)ret * fact[x] % P);
  		}
  		
  		out.println(ret);
  	}
  	
  	int go(int[] a) {
  		int[] dp = new int[a[0]];
  		dp[a[0] - 1] = 1;
  
  		int places = a[0] + 1;
  		
  		int toInsert = 0;
  		for (int x : a) {
  			toInsert += x;
  		}
  		toInsert -= a[0];
  
  		for (int i =1; i < a.length; i++) {
  
  			int here = a[i];
  			if (here == 0) {
  				continue;
  			}
  
  			int[] nxt = new int[dp.length + here];
  
  			for (int wasSame = 0; wasSame < dp.length; wasSame++) {
  				if (wasSame > toInsert) {
  					continue;
  				}
  				if (dp[wasSame] == 0) {
  					continue;
  				}
  
  				int wasDiff = places - wasSame;
  
  				for (int runsSame = 0; runsSame <= wasSame && runsSame <= here; runsSame++) {
  					for (int runsDiff = 0; runsDiff <= wasDiff && runsSame + runsDiff <= here; runsDiff++) {
  						if (runsSame + runsDiff == 0) {
  							continue;
  						}
  						int delta = (int) ((long) dp[wasSame]
  								* ways[wasSame][runsSame] % P * ways[wasDiff][runsDiff]
  								% P * ways[here - 1][runsSame + runsDiff - 1] % P);
  						if (delta == 0) {
  							continue;
  						}
  						int nxtIdx = (wasSame - runsSame) + (here - runsSame - runsDiff);
  						nxt[nxtIdx] += delta;
  						if (nxt[nxtIdx] >= P) {
  							nxt[nxtIdx] -= P;
  						}
  					}
  				}
  
  			}
  
  			dp = nxt;
  			places += here;
  			toInsert -= here;
  		}
  		
  //		System.err.println(Arrays.toString(a) + " " + idx);
  //		System.err.println(Arrays.toString(dp));
  		return dp[0];
  	}
  	
  	int[][] ways;
  	int[] fact;
  	static final int N = 350;
  	static final int P = 1_000_000_007;
  
  	void preCalc() {
  		ways = new int[N][];
  		for (int i = 0; i < N; i++) {
  			ways[i] = new int[i + 1];
  			ways[i][0] = ways[i][i] = 1;
  			for (int j = 1; j < i; j++) {
  				ways[i][j] = ways[i - 1][j] + ways[i - 1][j - 1];
  				if (ways[i][j] >= P) {
  					ways[i][j] -= P;
  				}
  			}
  		}
  		fact = new int[N];
  		fact[0] = 1;
  		for (int i = 1; i < N; i++) {
  			fact[i] = (int)((long)fact[i - 1] * i % P);
  		}
  	}
  
  	void stress() {
  
  	}
  
  	void test() {
  
  	}
  
  	C() throws IOException {
  		br = new BufferedReader(new InputStreamReader(System.in));
  		out = new PrintWriter(System.out);
  		preCalc();
  		submit();
  		//stress();
  		//test();
  		out.close();
  	}
  
  	static final Random rng = new Random();
  
  	static int rand(int l, int r) {
  		return l + rng.nextInt(r - l + 1);
  	}
  
  	public static void main(String[] args) throws IOException {
  		new C();
  	}
  
  	BufferedReader br;
  	PrintWriter out;
  	StringTokenizer st;
  
  	String nextToken() {
  		while (st == null || !st.hasMoreTokens()) {
  			try {
  				st = new StringTokenizer(br.readLine());
  			} catch (IOException e) {
  				throw new RuntimeException(e);
  			}
  		}
  		return st.nextToken();
  	}
  
  	String nextString() {
  		try {
  			return br.readLine();
  		} catch (IOException e) {
  			throw new RuntimeException(e);
  		}
  	}
  
  	int nextInt() {
  		return Integer.parseInt(nextToken());
  	}
  
  	long nextLong() {
  		return Long.parseLong(nextToken());
  	}
  
  	double nextDouble() {
  		return Double.parseDouble(nextToken());
  	}
  }
  