import java.util.*; import java.io.*; class Main { private static final void solve() throws IOException { final int n = ni(); final int m = (int) 2e5 + 1; var t = new int[m]; Arrays.fill(t, -1); var dsu = new DSU(n); var a = new int[n]; boolean two = false, thr = false; int one = 0; for (int i = 0; i < n; i++) { final int x = a[i] = ni(); if (x == 1) one++; two |= x % 2 == 0; thr |= x % 3 == 0; if (t[x] == -1) t[x] = i; else dsu.merge(t[x], i); } var pr = new boolean[m]; for (int i = 2; i < m; i++) { if (pr[i]) continue; int now = -1; for (int j = i; j < m; j += i) { pr[j] = true; if (t[j] != -1) { if (now == -1) now = t[j]; else dsu.merge(t[j], now); } } } var g = dsu.groups(); int size = g.size(); if (size == 1) { ou.println(2 * one); return; } if (one > 0) size += one - 1; if (two) { ou.println(2 * (size - 1)); return; } int ans = 2 * size; if (thr) ans = Math.min(ans, 3 * (size - 1)); ou.println(ans); return; } public static void main(String[] args) throws IOException { // for (int i = 0, t = ni(); i < t; i++) solve(); ou.flush(); } private static final int ni() throws IOException { return sc.nextInt(); } private static final int[] ni(int n) throws IOException { return sc.nextIntArray(n); } private static final long nl() throws IOException { return sc.nextLong(); } private static final long[] nl(int n) throws IOException { return sc.nextLongArray(n); } private static final String ns() throws IOException { return sc.next(); } private static final double nd() throws IOException { return sc.nextDouble(); } private static final ContestInputStream sc = new ContestInputStream(); private static final ContestOutputStream ou = new ContestOutputStream(); } class DSU { private int n; private int[] parentOrSize; public DSU(int n) { this.n = n; this.parentOrSize = new int[n]; java.util.Arrays.fill(parentOrSize, -1); } int merge(int a, int b) { if (!(0 <= a && a < n)) throw new IndexOutOfBoundsException("a=" + a); if (!(0 <= b && b < n)) throw new IndexOutOfBoundsException("b=" + b); int x = leader(a); int y = leader(b); if (x == y) return x; if (-parentOrSize[x] < -parentOrSize[y]) { int tmp = x; x = y; y = tmp; } parentOrSize[x] += parentOrSize[y]; parentOrSize[y] = x; return x; } boolean same(int a, int b) { if (!(0 <= a && a < n)) throw new IndexOutOfBoundsException("a=" + a); if (!(0 <= b && b < n)) throw new IndexOutOfBoundsException("b=" + b); return leader(a) == leader(b); } int leader(int a) { if (parentOrSize[a] < 0) { return a; } else { parentOrSize[a] = leader(parentOrSize[a]); return parentOrSize[a]; } } int size(int a) { if (!(0 <= a && a < n)) throw new IndexOutOfBoundsException("" + a); return -parentOrSize[leader(a)]; } ArrayList> groups() { int[] leaderBuf = new int[n]; int[] groupSize = new int[n]; for (int i = 0; i < n; i++) { leaderBuf[i] = leader(i); groupSize[leaderBuf[i]]++; } ArrayList> result = new ArrayList<>(n); for (int i = 0; i < n; i++) result.add(new ArrayList<>(groupSize[i])); for (int i = 0; i < n; i++) result.get(leaderBuf[i]).add(i); result.removeIf(ArrayList::isEmpty); return result; } } final class ContestInputStream extends FilterInputStream { protected final byte[] buf; protected int pos = 0; protected int lim = 0; private final char[] cbuf; public ContestInputStream() { super(System.in); this.buf = new byte[1 << 13]; this.cbuf = new char[1 << 20]; } boolean hasRemaining() throws IOException { if (pos < lim) return true; lim = in.read(buf); pos = 0; return lim > 0; } final int remaining() throws IOException { if (pos >= lim) { lim = in.read(buf); pos = 0; } return lim - pos; } @Override public final int available() throws IOException { if (pos < lim) return lim - pos + in.available(); return in.available(); } @Override public final long skip(long n) throws IOException { if (pos < lim) { int rem = lim - pos; if (n < rem) { pos += n; return n; } pos = lim; return rem; } return in.skip(n); } @Override public final int read() throws IOException { if (hasRemaining()) return buf[pos++]; return -1; } @Override public final int read(byte[] b, int off, int len) throws IOException { if (pos < lim) { int rem = Math.min(lim - pos, len); for (int i = 0; i < rem; i++) b[off + i] = buf[pos + i]; pos += rem; return rem; } return in.read(b, off, len); } public final char[] readToken() throws IOException { int cpos = 0; int rem; byte b; l: while ((rem = remaining()) > 0) { for (int i = 0; i < rem; i++) { b = buf[pos + i]; if (b <= 0x20) { pos += i + 1; cpos += i; if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a) pos++; break l; } cbuf[cpos + i] = (char) b; } pos += rem; cpos += rem; } char[] arr = new char[cpos]; for (int i = 0; i < cpos; i++) arr[i] = cbuf[i]; return arr; } public final int readToken(char[] cbuf, int off) throws IOException { int cpos = off; int rem; byte b; l: while ((rem = remaining()) > 0) { for (int i = 0; i < rem; i++) { b = buf[pos + i]; if (b <= 0x20) { pos += i + 1; cpos += i; if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a) pos++; break l; } cbuf[cpos + i] = (char) b; } pos += rem; cpos += rem; } return cpos - off; } public final int readToken(char[] cbuf) throws IOException { return readToken(cbuf, 0); } public final String next() throws IOException { int cpos = 0; int rem; byte b; l: while ((rem = remaining()) > 0) { for (int i = 0; i < rem; i++) { b = buf[pos + i]; if (b <= 0x20) { pos += i + 1; cpos += i; if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a) pos++; break l; } cbuf[cpos + i] = (char) b; } pos += rem; cpos += rem; } return String.valueOf(cbuf, 0, cpos); } public final char[] nextCharArray() throws IOException { return readToken(); } public final int nextInt() throws IOException { if (!hasRemaining()) return 0; int value = 0; byte b = buf[pos++]; if (b == 0x2d) { while (hasRemaining() && (b = buf[pos++]) > 0x20) value = value * 10 - b + 0x30; } else { do { value = value * 10 + b - 0x30; } while (hasRemaining() && (b = buf[pos++]) > 0x20); } if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a) pos++; return value; } public final long nextLong() throws IOException { if (!hasRemaining()) return 0L; long value = 0L; byte b = buf[pos++]; if (b == 0x2d) { while (hasRemaining() && (b = buf[pos++]) > 0x20) value = value * 10 - b + 0x30; } else { do { value = value * 10 + b - 0x30; } while (hasRemaining() && (b = buf[pos++]) > 0x20); } if (b == 0x0d && hasRemaining() && buf[pos] == 0x0a) pos++; return value; } public final char nextChar() throws IOException { if (!hasRemaining()) throw new EOFException(); final char c = (char) buf[pos++]; if (hasRemaining() && buf[pos++] == 0x0d && hasRemaining() && buf[pos] == 0x0a) pos++; return c; } public final float nextFloat() throws IOException { return Float.parseFloat(next()); } public final double nextDouble() throws IOException { return Double.parseDouble(next()); } public final boolean[] nextBooleanArray(char ok) throws IOException { char[] s = readToken(); int n = s.length; boolean[] t = new boolean[n]; for (int i = 0; i < n; i++) t[i] = s[i] == ok; return t; } public final boolean[][] nextBooleanMatrix(int h, int w, char ok) throws IOException { boolean[][] s = new boolean[h][]; for (int i = 0; i < h; i++) { char[] t = readToken(); int n = t.length; s[i] = new boolean[n]; for (int j = 0; j < n; j++) s[i][j] = t[j] == ok; } return s; } public final String[] nextStringArray(int len) throws IOException { String[] arr = new String[len]; for (int i = 0; i < len; i++) arr[i] = next(); return arr; } public final int[] nextIntArray(int len) throws IOException { int[] arr = new int[len]; for (int i = 0; i < len; i++) arr[i] = nextInt(); return arr; } public final int[] nextIntArray(int len, java.util.function.IntUnaryOperator map) throws IOException { int[] arr = new int[len]; for (int i = 0; i < len; i++) arr[i] = map.applyAsInt(nextInt()); return arr; } public final long[] nextLongArray(int len, java.util.function.LongUnaryOperator map) throws IOException { long[] arr = new long[len]; for (int i = 0; i < len; i++) arr[i] = map.applyAsLong(nextLong()); return arr; } public final int[][] nextIntMatrix(int h, int w) throws IOException { int[][] arr = new int[h][w]; for (int i = 0; i < h; i++) for (int j = 0; j < w; j++) arr[i][j] = nextInt(); return arr; } public final int[][] nextIntMatrix(int h, int w, java.util.function.IntUnaryOperator map) throws IOException { int[][] arr = new int[h][w]; for (int i = 0; i < h; i++) for (int j = 0; j < w; j++) arr[i][j] = map.applyAsInt(nextInt()); return arr; } public final long[] nextLongArray(int len) throws IOException { long[] arr = new long[len]; for (int i = 0; i < len; i++) arr[i] = nextLong(); return arr; } public final long[][] nextLongMatrix(int h, int w) throws IOException { long[][] arr = new long[h][w]; for (int i = 0; i < h; i++) for (int j = 0; j < w; j++) arr[i][j] = nextLong(); return arr; } public final float[] nextFloatArray(int len) throws IOException { float[] arr = new float[len]; for (int i = 0; i < len; i++) arr[i] = nextFloat(); return arr; } public final double[] nextDoubleArray(int len) throws IOException { double[] arr = new double[len]; for (int i = 0; i < len; i++) arr[i] = nextDouble(); return arr; } public final char[][] nextCharMatrix(int h, int w) throws IOException { char[][] arr = new char[h][]; for (int i = 0; i < h; i++) arr[i] = readToken(); return arr; } public final void nextThrow() throws IOException { next(); return; } public final void nextThrow(int n) throws IOException { for (int i = 0; i < n; i++) nextThrow(); return; } } final class ContestOutputStream extends FilterOutputStream implements Appendable { protected final byte[] buf; protected int pos = 0; public ContestOutputStream() { super(System.out); this.buf = new byte[1 << 13]; } @Override public void flush() throws IOException { out.write(buf, 0, pos); pos = 0; out.flush(); } void put(byte b) throws IOException { if (pos >= buf.length) flush(); buf[pos++] = b; } int remaining() throws IOException { if (pos >= buf.length) flush(); return buf.length - pos; } @Override public void write(int b) throws IOException { put((byte) b); } @Override public void write(byte[] b, int off, int len) throws IOException { int o = off; int l = len; while (l > 0) { int rem = Math.min(remaining(), l); for (int i = 0; i < rem; i++) buf[pos + i] = b[o + i]; pos += rem; o += rem; l -= rem; } } @Override public ContestOutputStream append(char c) throws IOException { put((byte) c); return this; } @Override public ContestOutputStream append(CharSequence csq, int start, int end) throws IOException { int off = start; int len = end - start; while (len > 0) { int rem = Math.min(remaining(), len); for (int i = 0; i < rem; i++) buf[pos + i] = (byte) csq.charAt(off + i); pos += rem; off += rem; len -= rem; } return this; } @Override public ContestOutputStream append(CharSequence csq) throws IOException { return append(csq, 0, csq.length()); } public ContestOutputStream append(char[] arr, int off, int len) throws IOException { int o = off; int l = len; while (l > 0) { int rem = Math.min(remaining(), l); for (int i = 0; i < rem; i++) buf[pos + i] = (byte) arr[o + i]; pos += rem; o += rem; l -= rem; } return this; } public ContestOutputStream print(char[] arr) throws IOException { return append(arr, 0, arr.length).newLine(); } public ContestOutputStream print(boolean value) throws IOException { if (value) return append("o"); return append("x"); } public ContestOutputStream println(boolean value) throws IOException { if (value) return append("o\n"); return append("x\n"); } public ContestOutputStream print(boolean[][] value) throws IOException { final int n = value.length, m = value[0].length; for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) print(value[i][j]); newLine(); } return this; } public ContestOutputStream print(int value) throws IOException { return append(String.valueOf(value)); } public ContestOutputStream println(int value) throws IOException { return append(String.valueOf(value)).newLine(); } public ContestOutputStream print(long value) throws IOException { return append(String.valueOf(value)); } public ContestOutputStream println(long value) throws IOException { return append(String.valueOf(value)).newLine(); } public ContestOutputStream print(float value) throws IOException { return append(String.valueOf(value)); } public ContestOutputStream println(float value) throws IOException { return append(String.valueOf(value)).newLine(); } private ContestOutputStream dtos(double x, int n) throws IOException { if (x < 0) { append('-'); x = -x; } x += Math.pow(10, -n) / 2; long longx = (long) x; print(longx); append('.'); x -= longx; for (int i = 0; i < n; i++) { x *= 10; int intx = (int) x; print(intx); x -= intx; } return this; } public ContestOutputStream print(double value) throws IOException { return dtos(value, 20); } public ContestOutputStream println(double value) throws IOException { return dtos(value, 20).newLine(); } public ContestOutputStream print(char value) throws IOException { return append(value); } public ContestOutputStream println(char value) throws IOException { return append(value).newLine(); } public ContestOutputStream print(String value) throws IOException { return append(value); } public ContestOutputStream println(String value) throws IOException { return append(String.valueOf(value)).newLine(); } public ContestOutputStream print(Object value) throws IOException { return append(String.valueOf(value)); } public ContestOutputStream println(Object value) throws IOException { return append(String.valueOf(value)).newLine(); } public ContestOutputStream printYN(boolean yes) throws IOException { if (yes) return println("Yes"); return println("No"); } public ContestOutputStream printAB(boolean yes) throws IOException { if (yes) return println("Alice"); return println("Bob"); } public ContestOutputStream print(CharSequence[] arr) throws IOException { if (arr.length > 0) { append(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').append(arr[i]); } return this; } public ContestOutputStream print(int[] arr) throws IOException { if (arr.length > 0) { print(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').print(arr[i]); } newLine(); return this; } public ContestOutputStream print(int[] arr, int length) throws IOException { if (length > 0) print(arr[0]); for (int i = 1; i < length; i++) append('\u0020').print(arr[i]); newLine(); return this; } public ContestOutputStream println(int[] arr) throws IOException { for (int i : arr) print(i).newLine(); return this; } public ContestOutputStream println(int[] arr, int length) throws IOException { for (int i = 0; i < length; i++) println(arr[i]); return this; } public ContestOutputStream print(boolean[] arr) throws IOException { if (arr.length > 0) { print(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').print(arr[i]); } newLine(); return this; } public ContestOutputStream print(long[] arr) throws IOException { if (arr.length > 0) { print(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').print(arr[i]); } newLine(); return this; } public ContestOutputStream print(long[] arr, int length) throws IOException { if (length > 0) print(arr[0]); for (int i = 1; i < length; i++) append('\u0020').print(arr[i]); newLine(); return this; } public ContestOutputStream println(long[] arr, int length) throws IOException { for (int i = 0; i < length; i++) println(arr[i]); return this; } public ContestOutputStream println(long[] arr) throws IOException { for (long i : arr) print(i).newLine(); return this; } public ContestOutputStream print(float[] arr) throws IOException { if (arr.length > 0) { print(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').print(arr[i]); } return this; } public ContestOutputStream println(float[] arr) throws IOException { for (float i : arr) print(i).newLine(); return this; } public ContestOutputStream print(double[] arr) throws IOException { if (arr.length > 0) { print(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').print(arr[i]); } return newLine(); } public ContestOutputStream println(double[] arr) throws IOException { for (double i : arr) print(i).newLine(); return this; } public ContestOutputStream print(Object[] arr) throws IOException { if (arr.length > 0) { print(arr[0]); for (int i = 1; i < arr.length; i++) append('\u0020').print(arr[i]); } return newLine(); } public ContestOutputStream print(java.util.ArrayList arr) throws IOException { if (!arr.isEmpty()) { final int n = arr.size(); print(arr.get(0)); for (int i = 1; i < n; i++) print(" ").print(arr.get(i)); } return newLine(); } public ContestOutputStream println(java.util.ArrayList arr) throws IOException { final int n = arr.size(); for (int i = 0; i < n; i++) println(arr.get(i)); return this; } public ContestOutputStream newLine() throws IOException { return append(System.lineSeparator()); } public ContestOutputStream endl() throws IOException { newLine().flush(); return this; } public ContestOutputStream print(int[][] arr) throws IOException { for (int[] i : arr) print(i); return this; } public ContestOutputStream print(long[][] arr) throws IOException { for (long[] i : arr) print(i); return this; } public ContestOutputStream print(char[][] arr) throws IOException { for (char[] i : arr) print(i); return this; } public ContestOutputStream print(Object[][] arr) throws IOException { for (Object[] i : arr) print(i); return this; } public ContestOutputStream println() throws IOException { return newLine(); } public ContestOutputStream println(Object... arr) throws IOException { for (Object i : arr) print(i); return newLine(); } public ContestOutputStream printToChar(int c) throws IOException { return print((char) c); } }