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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE MagicHash             #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings     #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeFamilies          #-}

import           Control.Applicative
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString             as B
import qualified Data.ByteString.Char8       as C
import qualified Data.ByteString.Unsafe      as B
import           Data.Char
import qualified Data.Foldable               as F
import           Data.Function
import qualified Data.IntMap.Strict          as IM
import qualified Data.IntSet                 as IS
import qualified Data.List                   as L
import qualified Data.Map.Strict             as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive.MutVar
import qualified Data.Set                    as S
import           Data.Tuple
import qualified Data.Vector                 as V
import qualified Data.Vector.Generic         as G
import qualified Data.Vector.Generic.Mutable as GM
import qualified Data.Vector.Unboxed         as U
import qualified Data.Vector.Unboxed.Mutable as UM
import           Debug.Trace
import           Foreign                     hiding (void)
import           GHC.Exts
import           Unsafe.Coerce

main :: IO ()
main = do
    n <- readLn :: IO Int
    cs <- L.unfoldr (C.readInt.C.dropWhile isSpace) <$> C.getContents
    print $ solve n cs

solve :: Int -> [Int] -> Int
solve n (x:xs) = runST $ do
    dp <- UM.replicate 200001 0

    UM.write dp x 1
    lastC <- foldlM (\ !prevC c -> do
        when (prevC /= c) $ do
            cur <- (+%) <$> UM.unsafeRead dp prevC <*> UM.unsafeRead dp c
            UM.unsafeWrite dp c cur
        return c
        ) x xs
    UM.unsafeRead dp lastC

-------------------------------------------------------------------------------
foldlM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
foldlM f a xs=foldr((>=>).flip f)return xs$a
{-# INLINE foldlM #-}

#define MOD 1000000007

modulus :: Int
modulus = MOD

infixr 8 ^%
infixl 7 *%, /%
infixl 6 +%, -%

type IntMod = Int

intMod :: Int -> IntMod
intMod x = mod x MOD

intModValidate :: Int -> Bool
intModValidate x = 0 <= x && x < MOD

(+%) :: IntMod -> IntMod -> IntMod
(I# x#) +% (I# y#) = case x# +# y# of
    r# | isTrue# (r# <# MOD#) -> I# r#
       | otherwise -> I# (r# -# MOD#)
{-# INLINE (+%) #-}

(-%) :: IntMod -> IntMod -> IntMod
(I# x#) -% (I# y#) = I# ((x# -# y# +# MOD#) `remInt#` MOD#)
{-# INLINE (-%) #-}

(*%) :: IntMod -> IntMod -> IntMod
(I# x#) *% (I# y#) = I# ((x# *# y#) `remInt#` MOD#)
{-# INLINE (*%) #-}

(/%) :: IntMod -> IntMod -> IntMod
(I# x#) /% (I# y#) = go# y# MOD# 1# 0#
  where
    go# a# b# u# v#
        | isTrue# (b# ># 0#) = case a# `quotInt#` b# of
            q# -> go# b# (a# -# (q# *# b#)) v# (u# -# (q# *# v#))
        | otherwise = I# ((x# *# (u# +# MOD#)) `remInt#` MOD#)
{-# INLINE (/%) #-}

(^%) :: IntMod -> Int -> IntMod
x ^% n
    | n > 0 = go 1 x n
    | n == 0 = 1
    | otherwise = go 1 (1 /% x) (-n)
  where
    go !acc !y !m
        | m .&. 1 == 0 = go acc (y *% y) (unsafeShiftR m 1)
        | m == 1 = acc *% y
        | otherwise = go (acc *% y) (y *% y) (unsafeShiftR (m - 1) 1)