source_code: import java.io.OutputStream;
  import java.io.IOException;
  import java.io.InputStream;
  import java.io.OutputStream;
  import java.io.PrintWriter;
  import java.util.Arrays;
  import java.io.BufferedWriter;
  import java.io.Writer;
  import java.io.OutputStreamWriter;
  import java.util.InputMismatchException;
  import java.io.IOException;
  import java.io.InputStream;
  
  /**
   * Built using CHelper plug-in
   * Actual solution is at the top
   */
  public class Main {
      public static void main(String[] args) {
          InputStream inputStream = System.in;
          OutputStream outputStream = System.out;
          InputReader in = new InputReader(inputStream);
          OutputWriter out = new OutputWriter(outputStream);
          TaskC solver = new TaskC();
          solver.solve(1, in, out);
          out.close();
      }
  
      static class TaskC {
          public int mod = 1000000007;
          public int MAXN = 333;
          public int[][] w1;
          public long[] fact;
          public long[] ifact;
  
          public void solve(int testNumber, InputReader in, OutputWriter out) {
              long[][] e = Factorials.getFIF(MAXN, mod);
              fact = e[0];
              ifact = e[1];
              w1 = new int[MAXN][MAXN];
              w1[0][0] = 1;
              for (int i = 1; i < MAXN; i++) {
                  for (int j = 1; j < MAXN; j++) {
                      for (int k = 1; k <= i; k++) {
                          w1[i][j] += w1[i - k][j - 1];
                          if (w1[i][j] >= mod) w1[i][j] -= mod;
                      }
                  }
              }
  
              int n = in.nextInt();
              int[] arr = in.readIntArray(n);
              boolean[] marked = new boolean[n];
              int[] fs = new int[n];
              int fidx = 0;
              for (int i = 0; i < n; i++) {
                  if (marked[i]) continue;
                  int count = 0;
                  for (int j = 0; j < n; j++) {
                      if (isSquare(1L * arr[i] * arr[j])) {
                          if (marked[j]) System.exit(1);
                          marked[j] = true;
                          count++;
                      }
                  }
                  fs[fidx++] = count;
              }
  
              fs = Arrays.copyOf(fs, fidx);
              long x = 1;
              for (int j : fs) x = x * fact[j] % mod;
              x = x * solve(fs) % mod;
              out.println(x);
          }
  
          public boolean isSquare(long x) {
              long d = (long) (Math.sqrt(x));
              while (d * d < x) d++;
              while (d * d > x) d--;
              return d * d == x;
          }
  
          public int solve(int[] freq) {
              int d = AUtils.sum(freq);
              int b = AUtils.max(freq);
              if (d == 0) return 1;
              if (b + b - 1 > d) return 0;
              int[] dp = new int[1];
              dp[0] = 1;
              for (int j = 0; j < freq.length; j++) {
                  if (freq[j] == 0) continue;
                  int[] nxt = new int[dp.length + freq[j]];
                  for (int pgr = 0; pgr < dp.length; pgr++) {
                      for (int cgr = 1; cgr <= freq[j]; cgr++) {
                          nxt[pgr + cgr] += 1L * dp[pgr] * w1[freq[j]][cgr] % mod * ifact[cgr] % mod;
                          if (nxt[pgr + cgr] >= mod) nxt[pgr + cgr] -= mod;
                      }
                  }
                  dp = nxt;
              }
  
              int res = 0;
              for (int i = 0; i < dp.length; i++) {
                  long x = 1L * dp[i] * fact[i] % mod;
                  if ((d - i) % 2 == 0) res += x;
                  else res -= x;
                  if (res >= mod) res -= mod;
                  if (res < 0) res += mod;
              }
              return res;
          }
  
      }
  
      static class InputReader {
          private InputStream stream;
          private byte[] buf = new byte[1024];
          private int curChar;
          private int numChars;
  
          public InputReader(InputStream stream) {
              this.stream = stream;
          }
  
          public int[] readIntArray(int tokens) {
              int[] ret = new int[tokens];
              for (int i = 0; i < tokens; i++) {
                  ret[i] = nextInt();
              }
              return ret;
          }
  
          public int read() {
              if (this.numChars == -1) {
                  throw new InputMismatchException();
              } else {
                  if (this.curChar >= this.numChars) {
                      this.curChar = 0;
  
                      try {
                          this.numChars = this.stream.read(this.buf);
                      } catch (IOException var2) {
                          throw new InputMismatchException();
                      }
  
                      if (this.numChars <= 0) {
                          return -1;
                      }
                  }
  
                  return this.buf[this.curChar++];
              }
          }
  
          public int nextInt() {
              int c;
              for (c = this.read(); isSpaceChar(c); c = this.read()) {
                  ;
              }
  
              byte sgn = 1;
              if (c == 45) {
                  sgn = -1;
                  c = this.read();
              }
  
              int res = 0;
  
              while (c >= 48 && c <= 57) {
                  res *= 10;
                  res += c - 48;
                  c = this.read();
                  if (isSpaceChar(c)) {
                      return res * sgn;
                  }
              }
  
              throw new InputMismatchException();
          }
  
          public static boolean isSpaceChar(int c) {
              return c == 32 || c == 10 || c == 13 || c == 9 || c == -1;
          }
  
      }
  
      static class AUtils {
          public static int max(int[] arr) {
              int res = arr[0];
              for (int x : arr) res = Math.max(res, x);
              return res;
          }
  
          public static int sum(int[] arr) {
              int sum = 0;
              for (int x : arr) {
                  sum += x;
              }
              return sum;
          }
  
      }
  
      static class Factorials {
          public static long[][] getFIF(int max, int mod) {
              long[] fact = new long[max];
              long[] ifact = new long[max];
              long[] inv = new long[max];
              inv[1] = 1;
              for (int i = 2; i < max; i++) {
                  inv[i] = (mod - mod / i) * inv[mod % i] % mod;
              }
              fact[0] = 1;
              ifact[0] = 1;
              for (int i = 1; i < max; i++) {
                  fact[i] = fact[i - 1] * i % mod;
                  ifact[i] = ifact[i - 1] * inv[i] % mod;
              }
              return new long[][]{fact, ifact, inv};
          }
  
      }
  
      static class OutputWriter {
          private final PrintWriter writer;
  
          public OutputWriter(OutputStream outputStream) {
              writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
          }
  
          public OutputWriter(Writer writer) {
              this.writer = new PrintWriter(writer);
          }
  
          public void close() {
              writer.close();
          }
  
          public void println(long i) {
              writer.println(i);
          }
  
      }
  }
  
  