Mike has a sequence A = [a1, a2, ..., an] of length n. He considers the sequence B = [b1, b2, ..., bn] beautiful if the gcd of all its elements is bigger than 1, i.e. <image>. 

Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index i (1 ≤ i < n), delete numbers ai, ai + 1 and put numbers ai - ai + 1, ai + ai + 1 in their place instead, in this order. He wants perform as few operations as possible. Find the minimal number of operations to make sequence A beautiful if it's possible, or tell him that it is impossible to do so.

<image> is the biggest non-negative number d such that d divides bi for every i (1 ≤ i ≤ n).

Input

The first line contains a single integer n (2 ≤ n ≤ 100 000) — length of sequence A.

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — elements of sequence A.

Output

Output on the first line "YES" (without quotes) if it is possible to make sequence A beautiful by performing operations described above, and "NO" (without quotes) otherwise.

If the answer was "YES", output the minimal number of moves needed to make sequence A beautiful.

Examples

Input

2
1 1


Output

YES
1


Input

3
6 2 4


Output

YES
0


Input

2
1 3


Output

YES
1

Note

In the first example you can simply make one move to obtain sequence [0, 2] with <image>.

In the second example the gcd of the sequence is already greater than 1. 
#include <bits/stdc++.h>
const double pi = acos(-1.0);
using namespace std;
inline long long MAX2(long long a, long long b) {
  return (a) > (b) ? (a) : (b);
}
inline long long MAX3(long long a, long long b, long long c) {
  return (a) > (b) ? ((a) > (c) ? (a) : (c)) : ((b) > (c) ? (b) : (c));
}
inline long long MIN2(long long a, long long b) {
  return (a) < (b) ? (a) : (b);
}
inline long long MIN3(long long a, long long b, long long c) {
  return (a) < (b) ? ((a) < (c) ? (a) : (c)) : ((b) < (c) ? (b) : (c));
}
int mod = 1e9 + 9;
int64_t extGcd(int64_t a, int64_t b, int64_t& x, int64_t& y) {
  if (!a) {
    x = 0;
    y = 1;
    return b;
  }
  int64_t x1, y1;
  int64_t d = extGcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
const int factRange = 1000000;
int fact[factRange];
inline int addMod(int a, int b, int m = mod) { return ((int64_t)a + b) % m; }
inline int mulMod(int a, int b, int m = mod) { return ((int64_t)a * b) % m; }
inline int divMod(int a, int b, int m = mod) {
  int64_t x, y;
  int64_t g = extGcd(b, m, x, y);
  if (g != 1) {
    cerr << "Bad gcd!" << '\n';
    for (;;)
      ;
  }
  x = (x % m + m) % m;
  return mulMod(a, x, m);
}
inline long long exp(long long a, long long b) {
  if (a == 0) return 0ll;
  long long r = 1LL;
  while (b > 0) {
    if (b & 1) {
      r = r * (a % mod);
      r = (r + mod) % mod;
    }
    b /= 2;
    a = (a % mod) * (a % mod);
    a = (a + mod) % mod;
  }
  return (r + mod) % mod;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  if (a == 0) return b;
  return gcd(b, a % b);
}
inline long long poww(long long a, long long b) {
  long long r = 1LL;
  while (b > 0) {
    if (b & 1) r = r * a;
    b /= 2;
    a = a * a;
  }
  return (long long)r;
}
unsigned long int setbits(long long n) {
  unsigned long int count = 0;
  while (n) {
    n &= (n - 1);
    count++;
  }
  return count;
}
int main() {
  int n;
  cin >> n;
  int a[n];
  long long curr = 0;
  for (long long i = (long long)(0); i < (long long)(n); i++) {
    cin >> a[i];
    curr = gcd(curr, a[i]);
  }
  if (curr > 1) {
    cout << "YES" << '\n' << 0 << '\n';
    return 0;
    ;
  }
  int ans = 0;
  for (int i = 0; i < n - 1; i++) {
    if (a[i] & 1 and a[i + 1] & 1) {
      ans++;
      a[i] = 2;
      a[i + 1] = 2;
    } else if (a[i] & 1 and a[i + 1] % 2 == 0) {
      ans += 2;
      a[i + 1] = 2;
    }
  }
  if (a[n - 1] % 2 != 0) ans += 2;
  cout << "YES" << '\n' << ans << '\n';
  return 0;
}
