Problem:
Score: 200 points

Problem Statement

You are an immigration officer in the Kingdom of AtCoder. The document carried by an immigrant has some number of integers written on it, and you need to check whether they meet certain criteria.

According to the regulation, the immigrant should be allowed entry to the kingdom if and only if the following condition is satisfied:

All even numbers written on the document are divisible by 3 or 5.

If the immigrant should be allowed entry according to the regulation, output APPROVED; otherwise, print DENIED.

Notes

The condition in the statement can be rephrased as "If x is an even number written on the document, x is divisible by 3 or 5".
Here "if" and "or" are logical terms.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq A_i \leq 1000

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

If the immigrant should be allowed entry according to the regulation, print APPROVED; otherwise, print DENIED.

Sample Input 1

5
6 7 9 10 31

Sample Output 1

APPROVED

The even numbers written on the document are 6 and 10.

All of them are divisible by 3 or 5, so the immigrant should be allowed entry.

Sample Input 2

3
28 27 24

Sample Output 2

DENIED

28 violates the condition, so the immigrant should not be allowed entry.

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io;
use io_ext::Reader;
use parse::ParseAll;

fn main() {
    let stdin = io::stdin();
    let mut r = Reader::new(stdin.lock());
    r.read_line();
    let a: Vec<i64> = r.read_line().split_whitespace().parse_all();
    let mut approved = true;
    for &i in &a {
        if i % 2 == 0 {
            if !(i % 3 == 0 || i % 5 == 0) {
                approved = false;
                break;
            }
        }
    }
    if approved {
        println!("APPROVED");
    } else {
        println!("DENIED");
    }
}

#[cfg(test)]
mod tests {
    use super::answer;

    #[test]
    fn test() {
        let digits = [1, 0, 0];
        let k = 1;
        assert_eq!(answer(&digits, k), 19);

        let digits = [2, 5];
        let k = 2;
        assert_eq!(answer(&digits, k), 14);

        let digits = [3, 1, 4, 1, 5, 9];
        let k = 2;
        assert_eq!(answer(&digits, k), 937);

        let digits: Vec<u8> = (0..100).map(|_| 9).collect();
        let k = 3;
        assert_eq!(answer(&digits, k), 117879300);
    }
}

pub mod int_ext {
    pub fn digits10(n: i64) -> i64 {
        assert!(n >= 0);

        let mut d = 1;
        let mut p = 10;
        while p <= n {
            p *= 10;
            d += 1;
        }
        d
    }

    pub fn permutation(n: i64, k: i64) -> i64 {
        assert!(k >= 0);
        assert!(n >= k);

        let mut p = 1;
        for i in 0..k {
            p = p * (n - i);
        }
        p
    }

    pub fn combination(n: i64, k: i64) -> i64 {
        use std::cmp;

        assert!(k >= 0);
        assert!(n >= k);

        let k = cmp::min(k, n - k);
        let num = permutation(n, k);
        let mut den = 1;
        for i in 0..k {
            den = den * (i + 1);
        }
        num / den
    }
}

/// A module for easy use of io.
pub mod io_ext {
    use std::io::BufRead;

    pub struct Reader<R> {
        buf: String,
        inner: R,
    }

    impl<R> Reader<R> {
        #[inline]
        pub fn new(inner: R) -> Self {
            Reader { buf: String::new(), inner: inner }
        }

        #[inline]
        pub fn into_inner(self) -> R {
            self.inner
        }
    }

    impl<R: BufRead> Reader<R> {
        #[allow(deprecated)]
        #[inline]
        pub fn read_line(&mut self) -> &str {
            self.buf.clear();
            self.inner.read_line(&mut self.buf).unwrap_or_else(|e| panic!("{}", e));
            self.buf.trim_right()
        }
    }
}

/// Parsing Iterator.
pub mod parse {
    use std::borrow::Borrow;
    use std::str::FromStr;

    pub trait FromStrIterator {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self;
    }

    pub trait ParseAll {
        fn parse_all<F: FromStrIterator>(self) -> F;
    }

    impl<S: Borrow<str>, I: Iterator<Item=S>> ParseAll for I {
        #[inline]
        fn parse_all<F: FromStrIterator>(self) -> F {
            F::from_str_iter(self)
        }
    }

    fn parse<S: Borrow<str>, I: Iterator<Item=S>, F: FromStr>(i: &mut I) -> F {
        i.next().unwrap_or_else(|| panic!("too few strings error")).borrow().parse().unwrap_or_else(|_| panic!("parse error"))
    }

    // To avoid conflict, this is not implemented for `A` but `(A,)`.
    impl<A: FromStr> FromStrIterator for (A, ) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, )
        }
    }

    impl<A: FromStr, B: FromStr> FromStrIterator for (A, B) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr> FromStrIterator for (A, B, C) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr, D: FromStr> FromStrIterator for (A, B, C, D) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            let d = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c, d)
        }
    }

    impl<T: FromStr> FromStrIterator for Vec<T> {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self {
            i.map(|s| s.borrow().parse().unwrap_or_else(|_| panic!("parse error"))).collect()
        }
    }
}

pub mod modulo {
    /// Returns `x` + `y` mod `modulo`.
    ///
    /// `x < modulo` and `y < modulo` must hold.
    #[inline]
    pub fn add(x: u32, y: u32, modulo: u32) -> u32 {
        debug_assert!(modulo > 0);
        debug_assert!(x < modulo && y < modulo);
        let sum = x as u64 + y as u64;
        if sum <= modulo as u64 {
            sum as u32
        } else {
            (sum as u32).wrapping_sub(modulo)
        }
    }

    /// Returns `x` - `y` mod `modulo`.
    ///
    /// `x < modulo` and `y < modulo` must hold.
    #[inline]
    pub fn sub(x: u32, y: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo);
        debug_assert!(x < modulo && y < modulo);
        if x >= y {
            x - y
        } else {
            modulo + x - y
        }
    }

    /// Returns `x` * `y` mod `modulo`.
    #[inline]
    pub fn mul(x: u32, y: u32, modulo: u32) -> u32 {
        ((x as u64 * y as u64) % modulo as u64) as u32
    }

    /// Returns `x`^ `y` mod `modulo`.
    pub fn pow(x: u32, mut y: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo);
        let mut p = x;
        let mut ret = 1;

        while y != 0 {
            if y & 1 == 1 {
                ret = mul(ret, p, modulo);
            }
            p = mul(p, p, modulo);
            y >>= 1;
        }
        ret
    }

    fn is_prime(x: u32) -> bool {
        let sqrt = (x as f32).sqrt() as u32;
        for factor in 2..sqrt {
            if x % factor == 0 {
                return false;
            }
        }
        true
    }

    /// Returns 1 / `x`.
    ///
    /// `modulo` must be a prime number.
    #[inline]
    fn reciprocal(x: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo && is_prime(modulo));
        pow(x, modulo - 2, modulo)
    }

    /// Returns `x` / `y` mod `modulo`.
    ///
    /// `modulo` must be a prime number.
    #[inline]
    pub fn div(x: u32, y: u32, modulo: u32) -> u32 {
        debug_assert!(0 < modulo && is_prime(modulo));
        mul(x, reciprocal(y, modulo), modulo)
    }

    /// Returns `n`P`k` mod `modulo`.
    pub fn perm(n: u32, k: u32, modulo: u32) -> u32 {
        let mut p = 1;
        for i in 0..k {
            p = mul(p, n - i, modulo);
        }
        p
    }

    /// Returns `n`C`k` mod `modulo`.
    pub fn comb(n: u32, k: u32, modulo: u32) -> u32 {
        let num = perm(n, k, modulo);
        let mut den = 1;
        for i in 0..k {
            den = mul(den, i + 1, modulo);
        }
        div(num, den, modulo)
    }
}