Problem: You are given an array of n integers. You need to split all integers into two groups so that the GCD of all integers in the first group is equal to one and the GCD of all integers in the second group is equal to one.

The GCD of a group of integers is the largest non-negative integer that divides all the integers in the group.

Both groups have to be non-empty.

Input

The first line contains a single integer n (2 ≤ n ≤ 10^5).

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — the elements of the array.

Output

In the first line print "YES" (without quotes), if it is possible to split the integers into two groups as required, and "NO" (without quotes) otherwise.

If it is possible to split the integers, in the second line print n integers, where the i-th integer is equal to 1 if the integer a_i should be in the first group, and 2 otherwise.

If there are multiple solutions, print any.

Examples

Input


4
2 3 6 7


Output


YES
2 2 1 1 


Input


5
6 15 35 77 22


Output


YES
2 1 2 1 1 


Input


5
6 10 15 1000 75


Output


NO

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
#pragma GCC optimize(2, 3, "Ofast")
using namespace std;
namespace MyMinMax {
template <typename T>
inline T mn(T x, T y) {
  return x < y ? x : y;
}
template <typename T>
inline T mx(T x, T y) {
  return x > y ? x : y;
}
template <typename T>
inline void chmin(T &x, T y) {
  (x > y) && (x = y);
}
template <typename T>
inline void chmax(T &x, T y) {
  (x < y) && (x = y);
}
}  // namespace MyMinMax
using namespace MyMinMax;
namespace IO {
char BB[1 << 18], *SS = BB, *TT = BB;
template <typename T>
inline void read(T &x) {
  x = 0;
  int fu = 1;
  char c =
      (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
           ? EOF
           : *SS++);
  while (c > 57 || c < 48) {
    if (c == 45) fu = -1;
    c = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
             ? EOF
             : *SS++);
  }
  while (c <= 57 && c >= 48) {
    x = x * 10 + c - 48;
    c = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
             ? EOF
             : *SS++);
  }
  x *= fu;
}
template <typename T>
inline void read(T *bg, T *ed) {
  while (bg != ed) read(*bg++);
}
inline void read(char &ch) {
  ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
            ? EOF
            : *SS++);
  while (ch <= 32)
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
}
inline void read(char *s) {
  char ch =
      (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
           ? EOF
           : *SS++);
  while (ch <= 32)
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  while (ch > 32)
    *s++ = ch,
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  *s = '\0';
}
inline void sread(char *s) {
  char ch =
      (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
           ? EOF
           : *SS++);
  while (ch < 32)
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  while (ch >= 32)
    *s++ = ch,
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  *s = '\0';
}
inline void pread(char *&s) {
  char ch =
      (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
           ? EOF
           : *SS++);
  while (ch <= 32)
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  while (ch > 32)
    *s++ = ch,
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  *s = '\0';
}
inline void spread(char *&s) {
  char ch =
      (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
           ? EOF
           : *SS++);
  while (ch < 32)
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  while (ch >= 32)
    *s++ = ch,
    ch = (SS == TT && (TT = (SS = BB) + fread(BB, 1, 1 << 18, stdin), SS == TT)
              ? EOF
              : *SS++);
  *s = '\0';
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
char out[1 << 18], *Out = out;
inline void putcha(char x) {
  *Out++ = x;
  if (Out - out >= (1 << 18)) fwrite(out, 1, Out - out, stdout), Out = out;
}
template <typename T>
inline void fprint(T x) {
  if (x < 0) putcha(45), x = -x;
  if (x > 9) fprint(x / 10);
  putcha(x % 10 + 48);
}
template <typename T>
inline void print(T x) {
  fprint(x);
  putcha(10);
}
inline void print(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
inline void print(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
}
inline void put(const char *ch) {
  while (*ch != '\0') putcha(*(ch++));
}
template <typename T, typename... Args>
inline void print(T x, Args... args) {
  fprint(x);
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename... Args>
inline void print(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(32);
  print(args...);
}
template <typename T, typename... Args>
inline void printl(T x, Args... args) {
  fprint(x);
  putcha(10);
  print(args...);
}
template <typename... Args>
inline void printl(const char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  print(args...);
}
template <typename... Args>
inline void printl(char *ch, Args... args) {
  while (*ch != '\0') putcha(*(ch++));
  putcha(10);
  print(args...);
}
template <typename T>
inline void sprint(T x) {
  fprint(x);
  putcha(32);
}
template <typename T, typename... Args>
inline void sprint(T x, Args... args) {
  fprint(x);
  putcha(32);
  sprint(args...);
}
template <typename T>
inline void sprint(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
}
template <typename T>
inline void print(T *bg, T *ed) {
  while (bg != ed) sprint(*bg++);
  putcha(10);
}
template <typename T>
inline void printl(T *bg, T *ed) {
  while (bg != ed) print(*bg++);
}
class AutoFlush {
 public:
  ~AutoFlush() { fwrite(out, 1, Out - out, stdout); }
} __AutoFlush;
}  // namespace IO
using namespace IO;
inline void swap(int &x, int &y) {
  int tmp = x;
  x = y;
  y = tmp;
}
namespace Orzlxl {
unsigned z3, z4, b;
inline unsigned rand_() {
  z3 = ((z3 & 4294967280U) << 7) ^ ((z3 << 13) ^ z3) >> 21;
  z4 = ((z4 & 4294967168U) << 13) ^ ((z4 << 3) ^ z4) >> 12;
  return (z3 ^ z4);
}
inline void srand_(unsigned x) {
  z3 = x ^ 0x1234598766U;
  z4 = (~x) + 51;
}
template <typename T>
inline void shuffle(T *bg, T *ed) {
  int len = ed - bg;
  for (int i = 1; i <= len - 1; ++i) swap(bg[i], bg[rand_() % i]);
}
}  // namespace Orzlxl
int a[100005], n, p[100005];
inline int gcd(int x, int y) { return !y ? x : gcd(y, x % y); }
inline int judge() {
  int ret = -1, num = 0;
  for (int i = 1; i <= n; ++i) {
    num = gcd(num, a[p[i]]);
    ret = i;
    if (num == 1) break;
  }
  if (ret == n) return -1;
  num = 0;
  for (int i = ret + 1; i <= n; ++i) {
    num = gcd(num, a[p[i]]);
    if (num == 1) return ret;
  }
  return -1;
}
int ans[100005];
int main() {
  Orzlxl ::srand_(20171302);
  read(n);
  read(a + 1, a + n + 1);
  int g = 0;
  for (int i = 1; i <= n; ++i) g = gcd(g, a[i]);
  if (g > 1) return puts("NO"), 0;
  for (int i = 1; i <= n; ++i) p[i] = i;
  while ((double)clock() / CLOCKS_PER_SEC <= 0.445) {
    Orzlxl ::shuffle(p + 1, p + n + 1);
    int res = judge();
    if (res == -1) continue;
    for (int i = 1; i <= res; ++i) ans[p[i]] = 1;
    for (int i = res + 1; i <= n; ++i) ans[p[i]] = 2;
    print("YES");
    print(ans + 1, ans + n + 1);
    return 0;
  }
  print("NO");
}