Problem: In a far away galaxy there is war again. The treacherous Republic made k precision strikes of power ai on the Empire possessions. To cope with the republican threat, the Supreme Council decided to deal a decisive blow to the enemy forces. 

To successfully complete the conflict, the confrontation balance after the blow should be a positive integer. The balance of confrontation is a number that looks like <image>, where p = n! (n is the power of the Imperial strike), <image>. After many years of war the Empire's resources are low. So to reduce the costs, n should be a minimum positive integer that is approved by the commanders.

Help the Empire, find the minimum positive integer n, where the described fraction is a positive integer.

Input

The first line contains integer k (1 ≤ k ≤ 106). The second line contains k integers a1, a2, ..., ak (1 ≤ ai ≤ 107).

Output

Print the minimum positive integer n, needed for the Empire to win.

Please, do not use the %lld to read or write 64-but integers in С++. It is preferred to use the cin, cout streams or the %I64d specificator.

Examples

Input

2
1000 1000


Output

2000

Input

1
2


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class htpe, class cmp>
using heap = priority_queue<htpe, vector<htpe>, cmp>;
template <class htpe>
using min_heap = heap<htpe, greater<htpe> >;
template <class htpe>
using max_heap = heap<htpe, less<htpe> >;
const int INF = 1791791791;
const long long INFLL = 1791791791791791791ll;
template <int input_buf_size, int output_buf_size>
class FastIO {
  char cbuf[input_buf_size + 1];
  int icur = 0;
  inline bool go_to_next_token() {
    while (cbuf[icur] == ' ' || cbuf[icur] == '\n') icur++;
    while (cbuf[icur] == 0) {
      icur = 0;
      if (fgets(cbuf, sizeof(cbuf), stdin) != cbuf) return false;
      while (cbuf[icur] == ' ' || cbuf[icur] == '\n') icur++;
    }
    return true;
  }

 public:
  string readString() {
    assert(go_to_next_token());
    string ans;
    while (cbuf[icur] != ' ' && cbuf[icur] != '\n' && cbuf[icur] != 0)
      ans.push_back(cbuf[icur++]);
    ans.shrink_to_fit();
    return ans;
  }
  template <class int_type>
  int_type readInt() {
    assert(go_to_next_token());
    int_type x = 0;
    bool m = cbuf[icur] == '-';
    if (m) icur++;
    while ('0' <= cbuf[icur] && cbuf[icur] <= '9') {
      x *= 10;
      x += (cbuf[icur] - '0');
      icur++;
    }
    if (m) x = -x;
    return x;
  }
  bool seekEof() { return !go_to_next_token(); }

 private:
  char obuf[output_buf_size + 1];
  int ocur = 0;
  inline void write_string(const char *str, size_t sz = 0) {
    if (sz == 0) sz = strlen(str);
    if (ocur + sz > output_buf_size) {
      fputs(obuf, stdout);
      fputs(str, stdout);
      ocur = 0;
      obuf[0] = 0;
      return;
    }
    strcpy(obuf + ocur, str);
    ocur += sz;
    obuf[ocur] = 0;
  }

 public:
  template <class int_type>
  void writeInt(int_type x, bool sp = true) {
    char buf[21];
    int c = 0;
    if (x < 0) {
      buf[c++] = '-';
      x = -x;
    }
    int s = c;
    if (x == 0) {
      buf[c++] = '0';
    }
    while (x > 0) {
      buf[c++] = (x % 10) + '0';
      x /= 10;
    }
    for (int i = 0; 2 * i < c - s; i++) {
      swap(buf[s + i], buf[c - 1 - i]);
    }
    buf[c] = 0;
    write_string(buf, c);
    if (sp) write_string(" ", 1);
  }
  void writeString(string s, bool space = true) {
    write_string(s.c_str(), s.size());
    if (space) write_string(" ", 1);
  }
  void writeEndl() { write_string("\n", 1); }
  void flush() {
    fputs(obuf, stdout);
    ocur = 0;
    obuf[0] = 0;
  }

 private:
  bool lflush;

 public:
  FastIO(bool local_flush) {
    obuf[0] = 0;
    lflush = local_flush;
  }
  ~FastIO() { fputs(obuf, stdout); }
};
FastIO<10000000, 10000000> IO(true);
long long numfct(long long n, long long p) {
  long long q = p;
  long long ans = 0;
  while (q <= n) {
    ans += n / q;
    q *= p;
  }
  return ans;
}
const int maxerat = 1e7 + 1;
int main() {
  int k = IO.readInt<int>();
  vector<int> a(k);
  for (int i = 0; i < ((int)(k)); ++i) {
    a[i] = IO.readInt<int>();
    assert(a[i] < maxerat);
  }
  vector<int> na(maxerat);
  for (int i = 0; i < ((int)(k)); ++i) na[a[i]]++;
  partial_sum((na).rbegin(), (na).rend(), na.rbegin());
  vector<int> primes;
  vector<long long> nums;
  bitset<maxerat> erat;
  erat.set();
  erat[0] = erat[1] = 0;
  for (int i = 0; i < ((int)(maxerat)); ++i) {
    if (erat[i]) {
      primes.push_back(i);
      for (int j = i; j < maxerat; j += i) {
        erat[j] = false;
      }
      nums.push_back(0);
      for (long long j = i; j < maxerat; j *= i) {
        for (int n = j; n < maxerat; n += j) {
          nums.back() += na[n];
        }
      }
    }
  }
  long long l = 0, r = 1LL * k * maxerat;
  while (l < r - 1) {
    long long mid = l + (r - l) / 2;
    bool f = true;
    for (int i = 0; i < ((int)(primes.size())); ++i) {
      if (nums[i] > numfct(mid, primes[i])) {
        f = false;
        break;
      }
    }
    if (f)
      r = mid;
    else
      l = mid;
  }
  IO.writeInt(r);
  IO.writeEndl();
  return 0;
}