You have a multiset containing several integers. Initially, it contains $a_1$ elements equal to $1$, $a_2$ elements equal to $2$, ..., $a_n$ elements equal to $n$.

You may apply two types of operations:  choose two integers $l$ and $r$ ($l \le r$), then remove one occurrence of $l$, one occurrence of $l + 1$, ..., one occurrence of $r$ from the multiset. This operation can be applied only if each number from $l$ to $r$ occurs at least once in the multiset;  choose two integers $i$ and $x$ ($x \ge 1$), then remove $x$ occurrences of $i$ from the multiset. This operation can be applied only if the multiset contains at least $x$ occurrences of $i$. 

What is the minimum number of operations required to delete all elements from the multiset?


-----Input-----

The first line contains one integer $n$ ($1 \le n \le 5000$).

The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($0 \le a_i \le 10^9$).


-----Output-----

Print one integer — the minimum number of operations required to delete all elements from the multiset.


-----Examples-----
Input
4
1 4 1 1

Output
2

Input
5
1 0 1 0 1

Output
3

Difficulty: interview

Starter code:

Solutions:

from sys import stdin

n = int(stdin.readline())
a = list(map(int,stdin.readline().split()))
a = [0] + a

ans = n

dp = [float("inf")] * (n+1)
dp[0] = 0
for i in range(1,n+1):

    nmin = float("inf")
    for j in range(i-1,-1,-1):
        if a[j] <= nmin:
            dp[i] = min(dp[i] , dp[j] + max(0,a[i]-a[j]) + (i-j-1) )
        nmin = min(nmin,a[j])

#print (dp)
for i in range(n+1):
    ans = min(ans , dp[i] + n-i)
print (ans)



n = int(input()) + 1
l = list(map(int, input().split())) + [0]
out = 0

q = []
for v in l:
    if v == 0:
        dp = []
        n = len(q)
        for i in range(n):
            curr = q[i] + i
            smol = q[i]
            for j in range(i - 1, -1, -1):
                smol = min(q[j], smol)
                diff = q[i] - smol
                curr = min(curr, diff + dp[j] + i - j - 1)
            dp.append(curr)
                
        real = [n - i + dp[i] - 1 for i in range(n)] + [n]
        out += min(real)
        q = []
    else:
        q.append(v)
print(out)