Problem:
Score : 700 points

Problem Statement

There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.

You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.

Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.

Constraints

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

0 \leq A_i \leq 10^9(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.

Sample Input 1

4
0
1
1
2

Sample Output 1

3

We can make X equal to A as follows:

Choose i=2. X becomes (0,0,1,0).

Choose i=1. X becomes (0,1,1,0).

Choose i=3. X becomes (0,1,1,2).

Sample Input 2

3
1
2
1

Sample Output 2

-1

Sample Input 3

9
0
1
1
0
1
2
2
1
2

Sample Output 3

8

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

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

import           Control.Applicative
import           Control.DeepSeq
import           Control.Exception
import           Control.Monad
import           Control.Monad.ST
import           Control.Monad.Trans.State.Strict
import           Data.Array.Base
import           Data.Array.ST                    (STUArray, runSTUArray)
import           Data.Bits
import           Data.Bool
import qualified Data.ByteString.Char8            as B
import           Data.Char
import           Data.Coerce
import qualified Data.Foldable                    as F
import           Data.Function
import           Data.Int
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 qualified Data.Set                         as S
import           Data.STRef
import           Data.Tuple
import           Data.Word
import           Debug.Trace
import           GHC.Arr                          (Array, Ix (..), STArray)
import           GHC.Exts
import           System.Exit
import           System.IO

main :: IO ()
main = do
    !n <- readLn :: IO Int
    xs <- L.unfoldr (B.readInt.B.dropWhile isSpace) <$> B.getContents
    print.maybe (-1) id $ solve n xs

solve n xs@(hd:_)
    | hd > 0 = Nothing
    | otherwise = go 0 0 n $ reverse xs
  where
    go !res !h !rest (0:xs)
        | h == 0 = go res 0 (rest - 1) xs
        | otherwise = Nothing
    go !res !h !rest (x:xs) = case compare h x of
        EQ -> go res (h - 1) (rest - 1) xs
        LT | x < rest -> go (res + x) (x - 1) (rest - 1) xs
        GT | x < rest -> go (res + x) (x - 1) (rest - 1) xs
        _  -> Nothing
    go res 0 _ [] = Just res
    go _ _ _ _ = Nothing