Problem:
Score : 300 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function setUp(input) {
  input = input.split("\n");
  N = Number(input[0].split(" ")[0]);
  AList = input[1].split(" ").map(function (d, i) {
    return Number(d);
  });
  main();
}
function main() {
  lawList = [];
  numList = [];
  AList.forEach(function (d, index) {
    var tmp = [];
    var value = d;
    for (var i = 2; i <= value;) {
      if (value % i === 0) {
        tmp.push(i);
        value = value / i;
        if (numList.indexOf(i) < 0) {
          numList.push(i);
        }
      } else {
        i++;
      }
    }
    lawList.push(tmp);
  });
  numList.sort(function (a, b) {
    return a - b;
  })

  var commonList = [];
  var numLen = numList.length;
  for (var numI = 0; numI < numLen;) {
    var num = numList[numI];
    var count = 0;
    lawList.forEach(function (arr, i) {
      if (arr.indexOf(num) >= 0) {
        count++;
      }
    });
    if (count === N) {
      commonList.push(num);
      lawList.forEach(function (arr, i) {
        arr.splice(arr.indexOf(num), 1);
      });
    } else {
      numI++;
    }
  }
  var len = N - 1;
  var max = 1;
  for (var j = 0; j <= len; j++) {
    var tmpMax = 1;
    var pointerArray = [];
    for (var numI = 0; numI < numLen;) {
      var num = numList[numI];
      var count = 0;
      lawList.forEach(function (arr, i) {
        if (i !== j) {
          var pointer = arr.indexOf(num);
          if (pointer >= 0) {
            var currentPointer = pointerArray[i];
            if (currentPointer === undefined || pointer > currentPointer) {
              count++;
            }
          }
        }
      });
      if (count === len) {
        tmpMax = tmpMax * num;
        lawList.forEach(function (arr, i) {
          pointerArray[i] = arr.indexOf(num);
        });
      } else {
        numI++;
      }
    }
    if (max < tmpMax) {
      max = tmpMax;
    }
  }
  commonList.forEach(function (d, i) {
    max = max * d;
  })
  console.log(max);
}

setUp(require("fs").readFileSync("/dev/stdin", "utf8"));
// setUp('2\n1000000000 1000000000')
// setUp('3\n12 15 18')