Problem:
Score : 300 points

Problem Statement

We have N clocks. The hand of the i-th clock (1≤i≤N) rotates through 360° in exactly T_i seconds.

Initially, the hand of every clock stands still, pointing directly upward.

Now, Dolphin starts all the clocks simultaneously.

In how many seconds will the hand of every clock point directly upward again?

Constraints

1≤N≤100

1≤T_i≤10^{18}

All input values are integers.

The correct answer is at most 10^{18} seconds.

Input

Input is given from Standard Input in the following format:

N
T_1
:
T_N

Output

Print the number of seconds after which the hand of every clock point directly upward again.

Sample Input 1

2
2
3

Sample Output 1

6

We have two clocks. The time when the hand of each clock points upward is as follows:

Clock 1: 2, 4, 6, ... seconds after the beginning

Clock 2: 3, 6, 9, ... seconds after the beginning

Therefore, it takes 6 seconds until the hands of both clocks point directly upward.

Sample Input 2

5
2
5
10
1000000000000000000
1000000000000000000

Sample Output 2

1000000000000000000

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
 
#define BIG 2000000007
 
#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;
 
typedef struct {
	int a;
	int b;
} hw;
 
#define N_MAX 100000
#define M_MAX 100000
 
ull n, m;
ull h, w;
int k;
ull va, vb, vc, vd, ve, vf;
ull a[N_MAX];
// sll a[N_MAX];
// ull b[N_MAX];
// ull dp[N_MAX][M_MAX + 1];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
hw arr[N_MAX];
hw brr[N_MAX];
// ull digitdp[102][   2][    2];
//          pos  less  carry
 
void swap_adj(ull *a, ull *b){
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}

ull divide(ull a, ull b){
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}
 
int digits(ull x){
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}
 
int min(ull x, ull y){
	return (x < y) ? x : y;
}
 
ull gcd(ull x, ull y){
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}
 
ull bitpow(ull a, ull x){
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= MOD;
		}
		x /= 2;
		a = (a * a) % MOD;
	}
	return result;
}

// int nextroute(int arr[]){
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;

// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];

// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }

int nibutan_target(ull target){
	ull maxdist = (target * (target + 1) / 2); // 時刻targetまでに到着できる距離は[-maxdist, maxdist]
	return (n <= maxdist);
}

int targetdig(ull x, int index /* 1-indexed */){
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int comp(const void *left, const void *right){
	if ((*(int*)left) < (*(int*)right)) {
		return -1;
	} else if ((*(int*)left) > (*(int*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int hwAcomp(const void *left, const void *right){
	return comp(&(((hw*)left)->a), &(((hw*)right)->a));
}

int hwBcomp(const void *left, const void *right){
	return comp(&(((hw*)left)->b), &(((hw*)right)->b));
}

int hwABcomp(const void *left, const void *right){
	int x = hwAcomp(left, right);
	if (x) return x;
	return hwBcomp(left, right);
}

int findarr(hw arr[], int length, int h, int w){
	int minok = length - 1;
	int minng = -1;

	while (minng + 1 < minok) {
		int med = (minok + minng) / 2;
		if (arr[med].a <= h) {
			minok = med;
		} else {
			minng = med;
		}
	}
	if (arr[minok].a != h) return 0;

	int maxok = minok;
	int maxng = length;

	while (maxok + 1 < maxng) {
		int med = (maxok + maxng) / 2;
		if (arr[med].a <= h) {
			maxok = med;
		} else {
			maxng = med;
		}
	}

	minok = minok;
	minng = maxok + 1;
	while (minok + 1 < minng) {
		int med = (maxok + maxng) / 2;
		if (arr[med].b < w) {
			minok = med;
		} else if (arr[med].b > w) {
			minng = med;
		} else {
			return 1;
		}
	}
	if (arr[minok].a != w) return 0;

	return 1;
}

ull solve(){
	int i, j;
	// int pos, less, carry;
	// const int posmax = strlen(s);
	// int stackmax = -1;
	ull result = 1;
	hw vector8[8] = {
		{-1, -1},
		{-1,  0},
		{-1, +1},
		{ 0, -1},
		{ 0, +1},
		{+1, -1},
		{+1,  0},
		{+1, +1}
	};

	for (i = 0; i < n; i++) {
		ull t;
		scanf("%llu", &t);
		result *= (t / gcd(result, t));
		// printf("%d: %llu\n", i, result);
	}

	printf("%llu\n", result);

	return 0;
}
 
int main(void){
	int i, j;
	int x;

	scanf("%llu", &n);

	solve();

	return 0;
}