Problem:
Score : 700 points

Problem Statement

There are N stones arranged in a row. The i-th stone from the left is painted in the color C_i.

Snuke will perform the following operation zero or more times:

Choose two stones painted in the same color. Repaint all the stones between them, with the color of the chosen stones.

Find the number of possible final sequences of colors of the stones, modulo 10^9+7.

Constraints

1 \leq N \leq 2\times 10^5

1 \leq C_i \leq 2\times 10^5(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
C_1
:
C_N

Output

Print the number of possible final sequences of colors of the stones, modulo 10^9+7.

Sample Input 1

5
1
2
1
2
2

Sample Output 1

3

We can make three sequences of colors of stones, as follows:

(1,2,1,2,2), by doing nothing.

(1,1,1,2,2), by choosing the first and third stones to perform the operation.

(1,2,2,2,2), by choosing the second and fourth stones to perform the operation.

Sample Input 2

6
4
2
5
4
2
4

Sample Output 2

5

Sample Input 3

7
1
3
1
2
3
3
2

Sample Output 3

5

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

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

use self::modint::ModInt;
mod modint {
    use std;
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt(usize);
    impl ModInt {
        pub fn new(value: usize) -> Self {
            ModInt(value % Self::modulo())
        }
        fn modulo() -> usize {
            1_000_000_007
        }
    }
    impl std::ops::Add for ModInt {
        type Output = Self;
        fn add(self, other: Self) -> Self {
            let mut value = self.0 + other.0;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Add<usize> for ModInt {
        type Output = Self;
        fn add(self, other: usize) -> Self {
            let mut value = self.0 + other;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Sub for ModInt {
        type Output = Self;
        fn sub(self, other: Self) -> Self {
            let mut value = self.0;
            if value < other.0 {
                value += Self::modulo();
            }
            value -= other.0;
            ModInt::new(value)
        }
    }
    impl std::ops::Sub<usize> for ModInt {
        type Output = Self;
        fn sub(self, other: usize) -> Self {
            let mut value = self.0;
            if value < other {
                value += Self::modulo();
            }
            value -= other;
            ModInt::new(value)
        }
    }
    impl std::ops::Mul for ModInt {
        type Output = Self;
        fn mul(self, other: Self) -> Self {
            let value = self.0 * other.0 % Self::modulo();
            ModInt::new(value)
        }
    }
    impl std::ops::Mul<usize> for ModInt {
        type Output = Self;
        fn mul(self, other: usize) -> Self {
            let value = self.0 * other % Self::modulo();
            ModInt::new(value)
        }
    }
    impl std::ops::Div for ModInt {
        type Output = Self;
        fn div(self, other: Self) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other.0;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Div<usize> for ModInt {
        type Output = Self;
        fn div(self, other: usize) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt::new(value)
        }
    }
    impl std::ops::AddAssign for ModInt {
        fn add_assign(&mut self, other: Self) {
            *self = *self + other;
        }
    }
    impl std::ops::AddAssign<usize> for ModInt {
        fn add_assign(&mut self, other: usize) {
            *self = *self + other;
        }
    }
    impl std::ops::SubAssign for ModInt {
        fn sub_assign(&mut self, other: Self) {
            *self = *self - other;
        }
    }
    impl std::ops::SubAssign<usize> for ModInt {
        fn sub_assign(&mut self, other: usize) {
            *self = *self - other;
        }
    }
    impl std::ops::MulAssign for ModInt {
        fn mul_assign(&mut self, other: Self) {
            *self = *self * other;
        }
    }
    impl std::ops::MulAssign<usize> for ModInt {
        fn mul_assign(&mut self, other: usize) {
            *self = *self * other;
        }
    }
    impl std::ops::DivAssign for ModInt {
        fn div_assign(&mut self, other: Self) {
            *self = *self / other;
        }
    }
    impl std::ops::DivAssign<usize> for ModInt {
        fn div_assign(&mut self, other: usize) {
            *self = *self / other;
        }
    }
    impl std::fmt::Debug for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
    impl std::fmt::Display for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
}

fn solve() {
    let n = get!(usize);
    let mut c = get!(usize; n);

    c.push(0);
    let mut map = BTreeMap::new();
    let mut dp = vec![ModInt::new(0); n+1];
    dp[0] = ModInt::new(1);
    for i in 0..n {
        if c[i] == c[i+1] {
            dp[i+1] = dp[i];
            continue;
        }
        *map.entry(c[i]).or_insert(ModInt::new(0)) += dp[i];
        if let Some(&val) = map.get(&c[i]) {
            dp[i+1] = val;
        }
    }
    println!("{}", dp[n]);
}