CF1824D LuoTianyi and the Function

LuoTianyi gives you an array $ a $ of $ n $ integers and the index begins from $ 1 $ . Define $ g(i,j) $ as follows: - $ g(i,j) $ is the largest integer $ x $ that satisfies $ \{a_p:i\le p\le j\}\subseteq\{a_q:x\le q\le j\} $ while $ i \le j $ ; - and $ g(i,j)=0 $ while $ i>j $ . There are $ q $ queries. For each query you are given four integers $ l,r,x,y $ , you need to calculate $ \sum\limits_{i=l}^{r}\sum\limits_{j=x}^{y}g(i,j) $ .

The first line contains two integers $ n $ and $ q $ ( $ 1\le n,q\le 10^6 $ ) — the length of the array $ a $ and the number of queries. The second line contains $ n $ integers $ a_1,a_2,\ldots,a_n $ ( $ 1\le a_i\le n $ ) — the elements of the array $ a $ . Next $ q $ lines describe a query. The $ i $ -th line contains four integers $ l,r,x,y $ ( $ 1\le l\le r\le n, 1\le x\le y\le n $ ) — the integers in the $ i $ -th query.

Print $ q $ lines where $ i $ -th line contains one integer — the answer for the $ i $ -th query.

In the first example: In the first query, the answer is $ g(1,4)+g(1,5)=3+3=6 $ . $ x=1,2,3 $ can satisfies $ \{a_p:1\le p\le 4\}\subseteq\{a_q:x\le q\le 4\} $ , $ 3 $ is the largest integer so $ g(1,4)=3 $ . In the second query, the answer is $ g(2,3)+g(3,3)=3+3=6 $ . In the third query, the answer is $ 0 $ , because all $ i > j $ and $ g(i,j)=0 $ . In the fourth query, the answer is $ g(6,6)=6 $ . In the second example: In the second query, the answer is $ g(2,3)=2 $ . In the fourth query, the answer is $ g(1,4)+g(1,5)=2+2=4 $ .