Problem:
Score : 300 points

Problem Statement

There are N monsters, numbered 1, 2, ..., N.

Initially, the health of Monster i is A_i.

Below, a monster with at least 1 health is called alive.

Until there is only one alive monster, the following is repeated:

A random alive monster attacks another random alive monster.

As a result, the health of the monster attacked is reduced by the amount equal to the current health of the monster attacking.

Find the minimum possible final health of the last monster alive.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible final health of the last monster alive.

Sample Input 1

4
2 10 8 40

Sample Output 1

2

When only the first monster keeps on attacking, the final health of the last monster will be 2, which is minimum.

Sample Input 2

4
5 13 8 1000000000

Sample Output 2

1

Sample Input 3

3
1000000000 1000000000 1000000000

Sample Output 3

1000000000

Solution in Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"log"
	"os"
	"strconv"
	"strings"
)

func main() {
	log.SetFlags(log.Lshortfile)
	nextReader = NewScanner()
	_ = nextInt()  //モンスターの数
	a := nextInt() // 各モンスターの体力
	if min(a...) == max(a...) {
		fmt.Println(max(a...))
		return
	}

	kisuflag := false
	gusuflag := false
	for _, v := range a {
		if v%2 == 0 {
			gusuflag = true
		} else {
			kisuflag = true
		}
	}

	if kisuflag && gusuflag {
		fmt.Println(1)
		return
	} else if gusuflag {
		fmt.Println(2)
		return
	}
}

// ------ Mathライブラリ ---------------------------------//
func max(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
		}
	}
	return r
}

func maxIdx(a ...int) int {
	r := a[0]
	index := 0
	for i := 0; i < len(a); i++ {
		if r < a[i] {
			r = a[i]
			index = i
		}
	}
	return index
}

func min(a ...int) int {
	r := a[0]
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
		}
	}
	return r
}

func minIdx(a ...int) int {
	r := a[0]
	index := 0
	for i := 0; i < len(a); i++ {
		if r > a[i] {
			r = a[i]
			index = i
		}
	}
	return index
}

func sum(a []int) (r int) {
	for i := range a {
		r += a[i]
	}
	return r
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// ------ Mathライブラリ ---------------------------------//

// ----- 標準入力用の関数 ----------------------------------//
var nextReader func() []string

func NewScanner() func() []string {
	r := bufio.NewScanner(os.Stdin)
	r.Buffer(make([]byte, 1024), int(1e+11))
	return func() []string {
		r.Scan()
		return strings.Fields(r.Text())
	}
}

func nextString() []string {
	return nextReader()
}

func nextInt() []int {
	var intArray []int
	strArray := nextReader()
	for _, v := range strArray {
		i, _ := strconv.Atoi(v)
		intArray = append(intArray, i)
	}
	return intArray
}

func nextFloat64() []float64 {
	var floatArray []float64
	strArray := nextReader()
	for _, v := range strArray {
		f, _ := strconv.ParseFloat(v, 64)
		floatArray = append(floatArray, f)
	}
	return floatArray
}

// ------ 標準入力用の関数 ---------------------------------//

// ------ あまり使わない -----------------------------------//
func nextInt64() []int64 {
	var int64Array []int64
	strArray := nextReader()
	for _, v := range strArray {
		i, _ := strconv.ParseInt(v, 10, 64)
		int64Array = append(int64Array, i)
	}
	return int64Array
}

// ------ あまり使わない -----------------------------------//