Problem:
Score : 300 points

Problem Statement

Given is a string S of length N-1.
Each character in S is < or >.

A sequence of N non-negative integers, a_1,a_2,\cdots,a_N, is said to be good when the following condition is satisfied for all i (1 \leq i \leq N-1):

If S_i= <: a_i<a_{i+1}

If S_i= >: a_i>a_{i+1}

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Constraints

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

S is a string of length N-1 consisting of < and >.

Input

Input is given from Standard Input in the following format:

S

Output

Find the minimum possible sum of the elements of a good sequence of N non-negative integers.

Sample Input 1

<>>

Sample Output 1

3

a=(0,2,1,0) is a good sequence whose sum is 3.
There is no good sequence whose sum is less than 3.

Sample Input 2

<>>><<><<<<<>>><

Sample Output 2

28

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;

#define scan(x) do{while((x=getchar())<'0'); for(x-='0'; '0'<=(_=getchar()); x=(x<<3)+(x<<1)+_-'0');}while(0)
char _;
#define complete_unique(a) a.erase(unique(a.begin(),a.end()),a.end())
#define all(a) a.begin(),a.end()
#define println printf("\n");
#define readln(x) getline(cin,x);
#define pb push_back
#define endl "\n"
#define INT_INF 0x3f3f3f3f
#define LL_INF 0x3f3f3f3f3f3f3f3f
#define MOD 1000000007
#define MOD2 1494318097
#define SEED 131
#define mp make_pair
#define fastio cin.tie(0); cin.sync_with_stdio(0);

#define MAXN 500005

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef unordered_map<int,int> umii;
typedef pair<int,int> pii;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef pair<int,pii> triple;
typedef int8_t byte;

mt19937 g1(time(0));

int randint(int a, int b){return uniform_int_distribution<int>(a, b)(g1);}
ll randlong(ll a,ll b){return uniform_int_distribution<long long>(a, b)(g1);}

ll gcd(ll a, ll b){return b == 0 ? a : gcd(b, a % b);}
ll lcm(ll a, ll b){return a*b/gcd(a,b);}
ll fpow(ll  b, ll exp, ll mod){if(exp == 0) return 1;ll t = fpow(b,exp/2,mod);if(exp&1) return t*t%mod*b%mod;return t*t%mod;}
ll divmod(ll i, ll j, ll mod){i%=mod,j%=mod;return i*fpow(j,mod-2,mod)%mod;}

int len,sum[MAXN],lst[MAXN];
char s[MAXN];
vector<pii> v;
ll res;

int main(){
	scanf("%s",s+1); len = (int)strlen(s+1);
	for(int i=1; i<=len; i++){
		if(s[i] == '<') sum[i] = sum[i-1]+1;
		else sum[i] = sum[i-1]-1;
	}
	int tmp = 1;
	for(int i=2; i<=len; i++){
		if(s[i] != s[i-1]){
			if(s[i-1] == '>'){
				for(int k=tmp; k<=i-1; k++)
					lst[k] = i-1;
			}
			tmp = i;
		}
	}
	if(s[len] == '>'){
		for(int k=tmp; k<=len; k++)
			lst[k] = len;
	}
	for(int i=1; i<=len; i++){
		if(s[i] == '>' && (i == 1 || s[i-1] == '<')){
			for(int k=i; k<=lst[i]; k++)
				sum[k] = sum[k-1]-1;
			int mx = 0;
			for(int k=lst[i]; k>=i; k--){
				if(sum[k]+mx >= 0){
					sum[k]+=mx; //res+=mx;
					continue;
				}
				mx = max(mx,-sum[k]);
				sum[k]+=mx;
//				res+=mx;
			}
			sum[i-1]+=mx;// res+=mx;
			mx = INT_MAX;
			for(int k=i-1; k<=lst[i]; k++)
				mx = min(mx,sum[k]);
			for(int k=i-1; k<=lst[i]; k++)
				sum[k]-=mx;
			sum[i-1] = max(sum[i-2]+1,sum[i-1]);
			i = lst[i];
		}else sum[i] = sum[i-1]+1;
//		printf("%d ",sum[i]);
	}
	for(int i=0; i<=len; i++){
		res+=sum[i];
//		printf("%d ",sum[i]);
	}
//	printf("\n");
	printf("%lld\n",res);
}